McCarthy, David and Mikkola, Kalle and Thomas, Teruji (2016): Utilitarianism with and without expected utility.
Preview 
PDF
MPRA_paper_79315.pdf Download (594kB)  Preview 
Abstract
We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal comparisons are encoded in a single `individual preorder'. The individual preorder then uniquely determines the social preorder. The theorems have features that may be considered characteristic of Harsanyistyle utilitarianism, such as indifference to ex ante and ex post equality. If in addition the individual preorder satisfies expected utility, the social preorder must be represented by expected total utility. In the constant population case, this is the conclusion of the social aggregation theorem of Harsanyi (1955) under anonymity, but contra Harsanyi, it is derived without assuming expected utility at the social level. However, the theorems are also consistent with the rejection of all of the expected utility axioms, at both the individual and social levels. Thus expected utility is inessential to Harsanyi's approach under anonymity. 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. We therefore give further results related to additional constraints on the individual preorder. First, stronger utilitarianfriendly assumptions, like Pareto or strong separability, are essentially equivalent to the main expected utility axiom of strong independence. Second, the individual preorder satisfies strong independence if and only if the social preorder has a mixturepreserving total utility representation; here the utility values can be taken as vectors in a preordered vector space, or more concretely as lexicographically ordered matrices of real numbers. Third, if the individual preorder satisfies a `local expected utility' condition popular in nonexpected utility theory, then the social preorder is `locally utilitarian'.
Item Type:  MPRA Paper 

Original Title:  Utilitarianism with and without expected utility 
Language:  English 
Keywords:  Harsanyi, utilitarianism, expected utility, nonexpected utility, egalitarianism, variable populations. 
Subjects:  D  Microeconomics > D6  Welfare Economics > D60  General D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice ; Clubs ; Committees ; Associations D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty 
Item ID:  79315 
Depositing User:  Dr David McCarthy 
Date Deposited:  23 May 2017 13:35 
Last Modified:  05 Oct 2019 17:12 
References:  Aliprantis, C. and K. Border Infinite Dimensional Analysis 3rd. ed. Springer, 2006. Allais, M. `The foundations of a positive theory of choice involving risk and a criticism of the postulates and axioms of the American school.' In M. Allais and O. Hagen eds. Expected Utility Hypothesis and the Allais Paradox, Dordrecht, Reidel, 1979: 27145. Alon, S. and G. Gayer `Utilitarian preferences with multiple priors' Econometrica, forthcoming. Anand, P. Foundations of Rational Choice Under Risk, Clarendon Press, Oxford, 1993. d'Aspremont, C. and L. Gevers `Equity and the informational basis of collective choice.' Review of Economic Studies 44: 199209. d'Aspremont, C. and L. Gevers `Social welfare functionals and interpersonal comparability.' In K. Arrow, A. Sen and K. Suzumura eds. Handbook of social choice and welfare Vol. 1, Amsterdam: North Holland, 2002: 459541. Aumann, R. `Utility theory without the completeness axiom.' Econometrica 30 (1962): 455462. Baucells M. and L. Shapley `Multiperson utility.' Tech Rep working paper No. 779, Department of Economics, UCLA, 1998. http://webprofesores.iese.edu/mbaucells Baucells, M. and L. S. Shapley `Multiperson utility.' Games and Economic Behavior 62 (2008): 329347. BenPorath, E., I. Gilboa, and D. Schmeidler `On the measurement of inequality under uncertainty.' Journal of Economic Theory 75 (1997): 194204. Billot, A. and V. Vergopoulos `Utilitarianism with prior heterogeneity' Documents de travail du Centre d'Economie de la Sorbonne (2014) 2014.49ISSN: 1955611X. 2014. <halshs01021399>. Blackorby, C. and D. Donaldson `A theoretical treatment of indices of absolute equality.' International Economic Review 21 (1980): 107136. Blackorby, C. and D. Donaldson `Social criteria for evaluating population change.' Journal of Public Economics 25: 1333. Blackorby, C., W. Bossert and D. Donaldson `Intertemporal population ethics: criticallevel utilitarian principles.' Econometrica 65 (1995): 13031320. Blackorby, C., W. Bossert and D. Donaldson `Uncertainty and criticallevel population principles.' Journal of Population Economics 11 (1998): 120. Blackorby, C, W. Bossert and D. Donaldson `Harsanyi's social aggregation theorem: a multiprofile approach with variablepopulation extensions.' Working paper. (2003) Departement de sciences economiques, Universite de Montreal. Blackorby, C, W. Bossert and D. Donaldson Population Issues in Social Choice Theory, Welfare Economics, and Ethics New York, Cambridge University Press, 2005. Blackorby, C, W. Bossert and D. Donaldson `Variablepopulation extensions of social aggregation theorems.' Social Choice and Welfare 28 (2007): 567589. Blume, L., A. Brandenburger, and E. Dekel `An overview of lexicographic choice under uncertainty.' Annals of Operations Research 19 (1989):231246. Bogachev, V. Measure Theory Springer, 2007. Border, K. `More on Harsanyi's utilitarian cardinal welfare function' Social Choice and Welfare 1 (1985): 279281. Bostrom, N. `Infinite ethics.' Analysis and Metaphysics 10 (2011): 959. Broome, J. (1989). `What's the good of equality?' Current Issues in Microeconomics. J. D. Hey ed., Macmillan: 236262. Broome, J. Weighing Goods Blackwell, Oxford, 1991. Broome, J. Ethics out of Economics Cambridge University Press, 1999. Broome, J. Weighing Lives New York, Oxford University Press, 2004. Brunnermeier, M., A. Simsek, W. Xiong `A welfare criterion for models with distorted beliefs' The Quarterly Journal of Economics 129(4) (2014): 17531797. Buchak, L. Risk and Rationality Oxford University Press, 2013. Bykvist, K. `The benefits of coming into existence.' Philosophical Studies 135 (2007): 335362. CerreiaVioglio, S., F. Maccheroni, and M. Marinacci `Stochastic dominance analysis without the independence axiom.' Management Science Published online: May 23, 2016 10.1287/mnsc.2015.2388 Chateauneuf, A. and M. Cohen `Riskseeking with diminishing marginal utility in a nonexpected utility model' Journal of Risk and Uncertainty 9 (1994): 7791. Chew, S. `Axiomatic Utility Theories with the Betweenness Property.' Annals of Operations Research 19 (1989): 273298. Chew, S., L. Epstein and U. Segal `Mixture Symmetry and Quadratic Utility' Econometrica 59(1) (1991):139163. Chew, S., E. Karni, and Z. Safra `Risk aversion in the theory of expected utility with rank dependent probabilities.' Journal of Economic Theory 42 (1987): 370381. Chew, S. and M. Mao `A Schur concave characterization of riskaversion for nonexpected utility preferences' Journal of Economic Theory 67 (1995): 402435. Chew, S. and N. Nishimura `Differentiability, comparative statics, and nonexpected utility preferences.' Journal of Economic Theory 56(2) (1992): 294312. Conrad, Paul F. `Embedding theorems for abelian groups with valuations', American Journal of Mathematics 75 (1953), 129. Coulhon, T. and P. Mongin, `Social choice theory in the case of von Neumann Morgenstern utilities' Social Choice and Welfare 6 (1989): 175187. Danan, E., T. Gajdos, B. Hill, J.M.Tallon `Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty' HEC Paris Research Paper No. ECO/SCD20141057, 2014. http://dx.doi.org/10.2139/ssrn.2468809 Danan, E., T. Gajdos, JM. Tallon (2015). `Harsanyi's aggregation theorem with incomplete preferences.' American Economic Journal: Microeconomics 7(1): 6169. De Meyer, B. and P. Mongin `A note on affine aggregation' Economics Letters 47 (1995): 177183. Diamond, P. `Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility: comment', Journal of Political Economy 75, (1967): 76566. Dillenberger, D. and R. Krishna `Expected utility without boundsa simple proof' Journal of Mathematical Economics 52 (2014): 143147. Domotor, Z. `Ordered sum and tensor product of linear utility structures.' Theory and Decision 11 (1979): 375399. Dravecky, J. `Spaces with measurable diagonal', Matematicky v Casopis 25.1, (1975): 39. Dubra, J. `Continuity and completeness under risk' Mathematical Social Sciences 61 (2011): 8081. Dubra, J., F. Maccheroni, and E. Ok `Expected utility theory without the completeness axiom.' Journal of Economic Theory 115 (2004): 118133. Epstein, L. and U. Segal (1992). `Quadratic social welfare.' Journal of Political Economy 61: 691712. Evren, O. `On the existence of expected multiutility representations.' Economic Theory 35(3): 575592. Fishburn, P. Utility Theory for Decision Making. New York, Wiley, 1970. Fishburn, P. Nonlinear Preference and Utility Theory, The John Hopkins University Press, 1988, Baltimore and London. Fleurbaey, M. `Two variants of Harsanyi's aggregation theorem' Economics Letters 105(3) (2009): 300302. Fleurbaey, M. `Assessing risky social situations', Journal of Political Economy, 118, (2010): 649680. Fleurbaey, M. and A. Voorhoeve `Priority or Equality for Possible People?', MS. Gilboa, I., D. Samet, and D. Schmeidler `Utilitarian aggregation of beliefs and tastes', Journal of Political Economy 112(4) (2004): 932 938 Grant, S., Kajii, A., Polak, B., and Safra, Z. `Generalized utilitarianism and Harsanyi's impartial observer theorem.' Econometrica 78(6) (2010): 19391971. Hadar, J. and W. Russell `Rules for ordering uncertain prospects.' American Economic Review 59 (1969): 2534. Hammond, P. `Consequentialist demographic norms and parenting rights.' Social Choice and Welfare 25 (1988): 127145. Hammond, P. `Interpersonal comparisons of utility: why and how they are and should be made', in Interpersonal Comparisons of WellBeing. J. Elster and J. Roemer eds. Cambridge University Press, 1991: 200254. Hammond, P. `Harsanyi's utilitarian theorem: A simpler proof and some ethical considerations', in R. Selten ed. Rational Interaction: Essays in Honor of John C. Harsanyi SpringerVerlag, Berlin, 1992. Hammond, P. `Objective expected utility: a consequentialist perspective'. In S. Barber{a, C. Seidel and P. Hammond eds. Handbook of Utility Theory, Vol. 1, Dordrecht: Kluwer, 1998: 145211. Harsanyi, J. `Cardinal utility in welfare economics and in the theory of risktaking', Journal of Political Economy 61 (1953): 434435. Harsanyi, J. `Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility' Journal of Political Economy 63 (1955): 30921. Harsanyi, J. `Morality and the theory of rational behavior.' Social Research 44, (1977): 62356. Harsanyi, J. Rational Behaviour and Bargaining Equilibrium in Games and Social Situations Cambridge, Cambridge University Press, 1977. Harsanyi, J. `Bayesian decision theory and utilitarian ethics' American Economic Review 68 (1978): 2238. Harsanyi, J. `Bayesian decision theory, rule utilitarianism, and Arrow's impossibility result' Theory and Decision 11 (1979): 289317. Hausner, M. `Multidimensional utilities.' In R. Thrall, C. Coombs and R. Davis eds. Decision Processes John Wiley, 1954. Hausner, M., and J. G. Wendel.`Ordered vector spaces', Proceedings of the American Mathematical Society 3 (1952): 977982. Hylland, A., and R. Zeckhauser `The impossibility of Bayesian group decision making with separate aggregation of beliefs and values.' Econometrica 47 (1979): 132136. Karni, E. and N. Zhou `Weighted utility theory with incomplete preferences'. manuscript, 2016. Kreps, D. Notes on the Theory of Choice, Westview Press, Boulder and London, 1988. Luce, R. and H. Raiffa Games and Decisions, John Wiley and Sons, New York, 1957. Machina, M. ``Expected utility' analysis without the independence axiom.' Econometrica 50: 277323. McCarthy, D. `Distributive equality.' Mind 124(496) (2015): 10451109. McCarthy, D.`The priority view' Economics and Philosophy, forthcoming. McCarthy, D., K. Mikkola, and T. Thomas `Aggregation for general populations without continuity or completeness'. Mimeo, 2016. McCarthy, D., and T. Thomas `Egalitarianism with risk'. Mimeo, 2016. Milgram, A. `Partially ordered sets, separating systems, and inductiveness'. In Reports of a Mathematical Colloquium, Second Series, Paris, University of Notre Dame, 1939: 1830. Mongin, P. `Harsanyi's aggregation theorem: multiprofile version and unsettled questions' Social Choice and Welfare 11(4) (1994): 331354. Mongin, P. `Consistent Bayesian aggregation', Journal of Economic Theory 66 (1995): 31351. Mongin, P. `Spurious unanimity and the Pareto principle' Economics and Philosophy (2015) DOI: http://dx.doi.org/10.1017/S0266267115000371. Published online: 26 November 2015 Mongin, P., and C. d'Aspremont `Utility theory and ethics' in S. Barbera, P. Hammond, and C. Seidl eds. Handbook of Utility Theory, vol. 1, Kluwer, Dordrecht, 233289, 1998. Mongin, P. and M. Pivato `Ranking multidimensional alternatives and uncertain prospects' Journal of Economic Theory 157 (2015): 146171. Myerson, R. `Utilitarianism, egalitarianism, and the timing effect in social choice problems' Econometrica 49 (1981): 883897. Ng, Y. `Some broader issues of social choice' in P. Pattanaik and M. Salles eds. Social Choice and Welfare. NorthHolland, Amsterdam, 1983, Chap. 9: 151173 Parfit, D. `Equality or priority?' Lindley Lectures Delivered at the University of. Kansas (Lawrence, Kansas: 1991. Reprinted in The Ideal of Equality. M. Clayton and A. Williams. eds. Macmillan, 2000: 81125. Parfit, D. Reasons and Persons New York, Oxford University Press, 1986. Pivato, M. `Risky social choice with incomplete or noisy interpersonal comparisons of wellbeing.' Social Choice and Welfare 40(1) (2013): 12339. Pivato, M. `Additive representation of separable preferences over infinite products.' Theory and Decision 77(1) (2014): 3183. Qu, X. `Separate aggregation of beliefs and values under ambiguity' Economic Theory 117. (First online: 22 December 2015). Richter, M. `Rational choice' in J. Chipman, L. Hurwicz, M. Richter, and H. Sonnenschein eds., Preferences, Utility, and Demand: A Minnesota Symposium, 1971, 2958. Harcourt Brace Jovanovich, New York. Rockafellar, R. Convex Analysis, Princeton, 1970. Rudin, W. Functional Analysis, 2nd. edition McGrawHill, 1991. Saito, K. `Social preferences under risk: equality of opportunity versus equality of outcome.' American Economic Review 103(7) (2013): 30843101. Schmidt, U. `Lottery dependent utility: a reexamination' Theory and Decision 50 (2001): 3558. Schmidt, U. `Alternatives to expected utility: some formal theories.' In S. Barbera, C. Seidel and P. Hammond eds. Handbook of Utility Theory, Vol. 2, Dordrecht: Kluwer, 2004: 757838. Sen, A. On Economic Inequality Oxford, Clarendon Press, 1973. Sen, A.`Welfare inequalities and Rawlsian axiomatics' Theory and Decision 7 (1976): 24362. Sen A. `Nonlinear social welfare functions: a reply to Professor Harsanyi' in R. Butts and J. Hintikka eds. Foundational Problems in the Special Sciences Dordrecht: Reidel, 1977: 297302. Sen, A. `On weights and measures: informational constraints in social welfare analysis.' Econometrica 45 (1977): 15391572. Sen, A. `Utilitarianism and welfarism.' Journal of Philosophy LXXVI (1979): 463489. Starmer, C. `Developments in nonexpected utility theory: the hunt for a descriptive theory of choice under risk.' Journal of Economic Literature 38(2) (2000): 332382. Tungodden, B. `The value of equality', Economics and Philosophy 19 (2003): 144. Wakker, P. `Separating marginal utility and probabilistic risk aversion.' Theory and Decision 36 (1994): 144. Wakker, P. Prospect Theory. Cambridge, Cambridge University Press, 2010. Weymark, J. `Generalized gini inequality indices.' Mathematical Social Sciences 1 (1981): 409430. Weymark, J. `A reconsideration of the HarsanyiSen debate on utilitarianism' in J. Elster and J. Roemer eds. Interpersonal Comparisons of WellBeing Cambridge University Press, 1991. Yaari, M. `The dual theory of choice under risk.'Econometrica 55 (1987): 95115. Zhou, L. `Harsanyi's utilitarianism theorems: general societies' Journal of Economic Theory, 72, (1997): 198207. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/79315 
Available Versions of this Item

Utilitarianism with and without expected utility. (deposited 20 Jul 2016 07:53)

Utilitarianism with and without expected utility. (deposited 10 Aug 2016 08:38)
 Utilitarianism with and without expected utility. (deposited 23 May 2017 13:35) [Currently Displayed]

Utilitarianism with and without expected utility. (deposited 10 Aug 2016 08:38)