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Abstract

We provide a general theorem on the aggregation of preferences under uncertainty. We study, in the Anscombe-Aumann setting a wide class of preferences, that includes most known models of decision under uncertainty (and state-dependent versions of these models). We prove that aggregation is possible and necessarily linear if (society's) preferences are "smooth". The latter means that society cannot have a non-neutral attitude towards uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate maxmin expected utility maximizers, even when they all have the same set of priors. We show that dropping a weak notion of monotonicity on society's preferences allows one to restore the possibility of aggregation of non-smooth preferences.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00193578.

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Date of creation: Feb 2005
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Handle: RePEc:hal:cesptp:halshs-00193578

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00193578
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Related research

Keywords: Aggregation; Harsanyi; uncertainty; multiple priors.;

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Find related papers by JEL classification:

• D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
• D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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1. Chambers, Christopher P. & Hayashi, Takashi, 2006. "Preference aggregation under uncertainty: Savage vs. Pareto," Games and Economic Behavior, Elsevier, vol. 54(2), pages 430-440, February.
   
   • Chambers, Christopher & Takashi Hayashi, 2003. "Preference Aggregation under Uncertainty: Savage vs. Pareto," Working Papers 1184, California Institute of Technology, Division of the Humanities and Social Sciences.
2. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
   
   • MONGIN, Philippe, 1993. "Consistent Bayesian Aggregation," CORE Discussion Papers 1993019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
3. Gilboa, I. & Samet, D. & Schmeidler, D., 2001. "Utilitarian Aggregation of Beliefs and Tastes," Papers 2001-17, Tel Aviv.
   
   • Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Utilitarian Aggregation of Beliefs and Tastes," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 932-938, August.
   • Itzhak Gilboa & Dov Samet & David Schmeidler, 2001. "Utilitarian Aggregation of Beliefs and Tastes," Game Theory and Information 0105001, EconWPA.
4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
   
   • David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
5. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
   
   • Ghirardato, Paolo & Marinacci, Massimo, 2000. "Risk, Ambigity and the Separation of Utility and Beliefs," Working Papers 1085, California Institute of Technology, Division of the Humanities and Social Sciences.
   • Massimo Marinacci & Paolo Ghirardato, 2001. "Risk, ambiguity, and the separation of utility and beliefs," ICER Working Papers - Applied Mathematics Series 21-2001, ICER - International Centre for Economic Research.
   • Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society.
6. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, vol. 47(2), pages 177-183, February.
   
   • DE MEYER, Bernard & MONGIN , Philippe, 1994. "A Note on Affine Aggregation," CORE Discussion Papers 1994014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
7. Charles Blackorby & David Donaldson & Philippe Mongin, 2004. "Social Aggregation Without the Expected Utility Hypothesis," Working Papers hal-00242932, HAL.
8. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
9. Charles Blackorby & David Donaldson, & John A. Weymark, 1997. "Social Aggregation and the Expected Utility Hypothesis," Old UBC Departmental Papers 9705, UBC Department of Economics.
   
   • Blackorby, C. & Donaldson, D. & Weymark, J.A., 1997. "Social Aggregation and the expected Utility Hypothesis," UBC Departmental Archives 97-5, UBC Department of Economics.
10. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309.

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Cited by:

1. Marcello Basili, 2008. "The global strategy to cope with H5N1: the property rights caveat," Department of Economic Policy, Finance and Development (DEPFID) University of Siena 0908, Department of Economic Policy, Finance and Development (DEPFID), University of Siena.
2. Christian Gollier, 2007. "Whom should we believe? Aggregation of heterogeneous beliefs," Journal of Risk and Uncertainty, Springer, vol. 35(2), pages 107-127, October.

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