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Representation and aggregation of preferences under uncertainty

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  • Gajdos, T.
  • Tallon, J.-M.
  • Vergnaud, J.-C.

Abstract

We axiomatize in the Anscombe-Aumann setting a wide class of preferences called rank-dependent additive preferences that includes most known models of decision under uncertainty as well as state dependent versions of these models. We prove that aggregation is possible and necessarily linear if and only if (society's) preferences are uncertainty neutral. The latter means that society cannot have a non-neutral attitude toward uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate multiple prior agents, even when they all have the same set of priors. A number of ways to restore the possibility of aggregation are then discussed.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 141 (2008)
Issue (Month): 1 (July)
Pages: 68-99

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Handle: RePEc:eee:jetheo:v:141:y:2008:i:1:p:68-99

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. Mongin, P., . "Consistent Bayesian aggregation," CORE Discussion Papers RP -1176, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2005. "Certainty Independence and the Separation of Utility and Beliefs," Journal of Economic Theory, Elsevier, vol. 120(1), pages 129-136, January.
  3. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  4. 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.
  5. MONGIN, Philippe, 1996. "The Paradox of the Bayesian Experts and State-Dependent Utility Theory," CORE Discussion Papers 1996026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Peter A. Diamond, 1967. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utility: Comment," Journal of Political Economy, University of Chicago Press, vol. 75, pages 765.
  7. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  8. Hylland, Aanund & Zeckhauser, Richard J, 1979. "The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values," Econometrica, Econometric Society, vol. 47(6), pages 1321-36, November.
  9. 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.
  10. 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.
  11. 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.
  12. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, vol. 47(2), pages 177-183, February.
  13. Epstein, Larry G & Segal, Uzi, 1992. "Quadratic Social Welfare Functions," Journal of Political Economy, University of Chicago Press, vol. 100(4), pages 691-712, August.
  14. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
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Citations

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Cited by:
  1. Mongin, Philippe & Pivato, Marcus, 2012. "Ranking Multidimensional Alternatives and Uncertain Prospects," MPRA Paper 42515, University Library of Munich, Germany.
  2. repec:hal:journl:halshs-00768894 is not listed on IDEAS
  3. Hervé Crès & Itzhak Gilboa, & Nicolas Vieille, 2011. "Aggregation of multiple prior opinions," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
  4. Hill, Brian, 2012. "Unanimity and the aggregation of multiple prior opinions," Les Cahiers de Recherche 959, HEC Paris.
  5. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2013. "Harsanyi's aggregation theorem with incomplete preferences," THEMA Working Papers 2013-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  6. repec:hal:cesptp:hal-00443075 is not listed on IDEAS
  7. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer, vol. 41(2), pages 427-452, July.
  8. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
  9. Frederik Herzberg, 2013. "Aggregation of Monotonic Bernoullian Archimedean preferences: Arrovian impossibility results," Working Papers 488, Bielefeld University, Center for Mathematical Economics.
  10. Herzberg, Frederik, 2013. "Arrovian aggregation of MBA preferences: An impossibility result," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79957, Verein für Socialpolitik / German Economic Association.
  11. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
  12. Chew, Soo Hong & Sagi, Jacob S., 2012. "An inequality measure for stochastic allocations," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1517-1544.

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