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Aggregation of multiple prior opinions

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Author Info

  • Crès, Hervé
  • Gilboa, Itzhak
  • Vieille, Nicolas

Abstract

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision makerʼs 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 makerʼs set of priors is precisely all the weighted-averages of priors, where an expertʼs prior is taken from her set and the weight vector is taken from Λ; (ii) the decision makerʼs valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the expertsʼ valuations.

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Bibliographic Info

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

Volume (Year): 146 (2011)
Issue (Month): 6 ()
Pages: 2563-2582

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Handle: RePEc:eee:jetheo:v:146:y:2011:i:6:p:2563-2582

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

Related research

Keywords: Aggregation of opinions; Ambiguity; Multiple priors;

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References

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  1. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  2. 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.
  3. 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.
  4. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer, vol. 41(2), pages 427-452, July.
  5. repec:hal:cesptp:halshs-00451982 is not listed on IDEAS
  6. Bossert, W., 1996. "Uncertainty Aversion in Nonprobabilistic Decision Models," Working Papers 9609, University of Waterloo, Department of Economics.
  7. 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.
  8. 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.
  9. 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.
  10. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  11. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, October.
  12. repec:hal:journl:halshs-00266049 is not listed on IDEAS
  13. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, 09.
  14. MONGIN, Philippe, 1993. "Consistent Bayesian Aggregation," CORE Discussion Papers 1993019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2008. "Probabilities in Economic Modelling," Levine's Working Paper Archive 122247000000001976, David K. Levine.
  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.
  17. 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.
  18. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
  19. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
  20. 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.
  21. repec:hal:journl:halshs-00451982 is not listed on IDEAS
  22. 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.
  23. 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.
  24. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  25. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
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Citations

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Cited by:
  1. repec:hal:cesptp:hal-00443075 is not listed on IDEAS
  2. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer, vol. 41(2), pages 427-452, July.
  3. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
  4. Hill, Brian, 2012. "Unanimity and the aggregation of multiple prior opinions," Les Cahiers de Recherche 959, HEC Paris.
  5. 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.
  6. Mongin, Philippe & Pivato, Marcus, 2012. "Ranking Multidimensional Alternatives and Uncertain Prospects," MPRA Paper 42515, University Library of Munich, Germany.
  7. 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.

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