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Aggregation of multiple prior opinions

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Author Info

  • Itzhak Gilboa,

    (Groupement de Recherche et d'Etudes en Gestion à HEC)

  • Nicolas Vieille

    (Groupement de Recherche et d'Etudes en Gestion à HEC)

  • Hervé Crès

    (Département d'économie)

Abstract

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker’s utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker’s set of priors is precisely all the weighted-averages of priors, where an expert’s prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker’s valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts’ valuations.

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Bibliographic Info

Paper provided by Sciences Po in its series Sciences Po publications with number info:hdl:2441/eu4vqp9ompqllr09iepso50rh.

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Date of creation: 2011
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Publication status: Published in Journal of Public Economic Theory, 2011
Handle: RePEc:spo:wpmain:info:hdl:2441/eu4vqp9ompqllr09iepso50rh

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Related research

Keywords: Aggregation of opinions; Ambiguity; Multiple priors;

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References

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  1. 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.
  2. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
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  4. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, October.
  5. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series 11-2003, ICER - International Centre for Economic Research, revised Apr 2003.
  6. Bossert, W., 1996. "Uncertainty Aversion in Nonprobabilistic Decision Models," Working Papers 9609, University of Waterloo, Department of Economics.
  7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  8. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  9. Mongin, P., . "Consistent Bayesian aggregation," CORE Discussion Papers RP -1176, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  11. 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.
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  14. Walter Bossert & Arkadii Slinko, 2006. "Relative uncertainty aversion and additively representable set rankings," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(2), pages 105-122.
  15. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2007. "Probabilities in Economic Modeling," Levine's Bibliography 843644000000000357, UCLA Department of Economics.
  16. 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.
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  18. 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.
  19. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, 09.
  20. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer, vol. 41(2), pages 427-452, July.
  21. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  22. Chambers, Christopher P. & Echenique, Federico, . "When does aggregation reduce uncertainty aversion?," Working Papers 1299, California Institute of Technology, Division of the Humanities and Social Sciences.
  23. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
  24. Itzhak Gilboa & Dov Samet & David Schmeidler, 2001. "Utilitarian Aggregation of Beliefs and Tastes," Game Theory and Information 0105001, EconWPA.
  25. 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.
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Citations

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Cited by:
  1. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer, vol. 41(2), pages 427-452, July.
  2. Laure Cabantous & Denis Hilton & Howard Kunreuther & Erwann Michel-Kerjan, 2011. "Is imprecise knowledge better than conflicting expertise? Evidence from insurers’ decisions in the United States," Journal of Risk and Uncertainty, Springer, vol. 42(3), pages 211-232, June.
  3. Aurélien Baillon & Laure Cabantous & Peter Wakker, 2012. "Aggregating imprecise or conflicting beliefs: An experimental investigation using modern ambiguity theories," Journal of Risk and Uncertainty, Springer, vol. 44(2), pages 115-147, April.
  4. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
  5. Hill, Brian, 2012. "Unanimity and the aggregation of multiple prior opinions," Les Cahiers de Recherche 959, HEC Paris.
  6. Mongin, Philippe & Pivato, Marcus, 2012. "Ranking Multidimensional Alternatives and Uncertain Prospects," MPRA Paper 42515, University Library of Munich, Germany.

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