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Unanimity and the aggregation of multiple prior opinions

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Author Info

  • Hill, Brian

    ()
    (Hec Paris)

Abstract

Author's abstract. In a situation of decision under uncertainty, a decision maker wishes to choose according to the maxmin expected utility rule, and he can observe the preferences of a set of experts who all share his utility function and all use the maxmin EU rule. This paper considers rules for aggregating the experts’ sets of priors into a set that the decision maker can use. It is shown that, in a multi profile setting, among the rules that allow the decision maker’s evaluation of an act to depend only on the experts'evaluations of that act, the only rule satisfying the standard unanimity or Pareto condition on preferences is the “set of weights” aggregation rule, according to which the decision maker’s set of priors is the set of weighted averages of the priors in the experts’ sets, with the weights taken from a set  of probability vectors over the experts. An analogous characterisation is obtained for variational preferences.

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Bibliographic Info

Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 959.

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Length: 26 pages
Date of creation: 19 Jan 2012
Date of revision:
Handle: RePEc:ebg:heccah:0959

Contact details of provider:
Postal: HEC Paris, 78351 Jouy-en-Josas cedex, France
Web page: http://www.hec.fr/
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Related research

Keywords: aggregation of beliefs; opinion pooling; ambiguity; multiple priors; pareto condition; variational preferences;

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References

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  1. 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.
  2. Itzhak Gilboa, & Nicolas Vieille & Hervé Crès, 2011. "Aggregation of multiple prior opinions," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
  3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  4. MONGIN, Philippe, 1993. "Consistent Bayesian Aggregation," CORE Discussion Papers 1993019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. repec:hal:cesptp:halshs-00266049 is not listed on IDEAS
  6. Gajdos, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Representation and aggregation of preferences under uncertainty," Journal of Economic Theory, Elsevier, vol. 141(1), pages 68-99, July.
  7. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
  8. Gilboa, Itzhak & Postlewaite, Andrew & Schmeidler, David, 2009. "Is It Always Rational To Satisfy Savage'S Axioms?," Economics and Philosophy, Cambridge University Press, vol. 25(03), pages 285-296, November.
  9. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer, vol. 41(2), pages 427-452, July.
  10. Hill, Brian, 2013. "Confidence and decision," Games and Economic Behavior, Elsevier, vol. 82(C), pages 675-692.
  11. repec:hal:journl:halshs-00266049 is not listed on IDEAS
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