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On the impossibility of preference aggregation under uncertainty

  • Thibault Gajdos


    (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Panthéon-Sorbonne - CNRS)

  • Jean-Marc Tallon


    (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Panthéon-Sorbonne - CNRS)

  • Jean-Christophe Vergnaud


    (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Panthéon-Sorbonne - CNRS)

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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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
Date of revision:
Publication status: Published in Cahiers de la Maison des Sciences Economiques 2005.12 - ISSN : 1624-0340. 2005
Handle: RePEc:hal:cesptp:halshs-00193578
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  1. 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.
  2. Charles Blackorby & David Donaldson & Philippe Mongin, 2004. "Social Aggregation Without the Expected Utility Hypothesis," Working Papers hal-00242932, HAL.
  3. Mongin, P., . "Consistent Bayesian aggregation," CORE Discussion Papers RP 1176, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, vol. 47(2), pages 177-183, February.
  5. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
  6. Gilboa, I. & Samet, D. & Schmeidler, D., 2001. "Utilitarian Aggregation of Beliefs and Tastes," Papers 2001-17, Tel Aviv.
  7. 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.
  8. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  9. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
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