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Unanimity and the aggregation of multiple prior opinions

Author

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  • Brian Hill

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Brian Hill, 2012. "Unanimity and the aggregation of multiple prior opinions," Working Papers hal-00712015, HAL.
    • Handle: RePEc:hal:wpaper:hal-00712015
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    References listed on IDEAS

    as
    1. Hervé Crès & Itzhak Gilboa & Nicolas Vieille, 2011. "Aggregation of multiple prior opinions," Post-Print hal-00656618, HAL.
    2. 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.
    3. ,, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
    4. 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.
    5. Gilboa, Itzhak & Postlewaite, Andrew & Schmeidler, David, 2009. "Is It Always Rational To Satisfy Savage'S Axioms?," Economics and Philosophy, Cambridge University Press, vol. 25(3), pages 285-296, November.
    6. Crès, Hervé & Gilboa, Itzhak & Vieille, Nicolas, 2011. "Aggregation of multiple prior opinions," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2563-2582.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Hill, Brian, 2013. "Confidence and decision," Games and Economic Behavior, Elsevier, vol. 82(C), pages 675-692.
    9. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 427-452, July.
    10. 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.
    11. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
    12. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    13. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
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    Cited by:

    1. Hill , Brian & Danan , Eric, 2014. "Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty," HEC Research Papers Series 1057, HEC Paris.
    2. repec:hal:pseose:halshs-01415412 is not listed on IDEAS
    3. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2016. "Robust Social Decisions," American Economic Review, American Economic Association, vol. 106(9), pages 2407-2425, September.

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    More about this item

    Keywords

    Aggregation of beliefs; Opinion pooling; Ambiguity; Multiple priors; Pareto condition; Variational preferences;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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