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Aggregation of multiple prior opinions

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Author Info

  • Hervé Crès

    (Département d'économie)

  • Itzhak Gilboa,

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

  • Nicolas Vieille

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

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
Date of revision:
Publication status: Published in Journal of Public Economic Theory, 2011, vol. 146, pp.2563-2582
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. Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2006. "Attitude toward imprecise information," Cahiers de la Maison des Sciences Economiques v06081, Université Panthéon-Sorbonne (Paris 1).
  2. Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2007. "Probabilities in Economic Modeling," PIER Working Paper Archive 07-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  3. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  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. Mongin, P., . "Consistent Bayesian aggregation," CORE Discussion Papers RP -1176, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  7. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
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  9. BOSSERT, Walter & SLINKO, Arkadii, 2004. "Relative Uncertainty Aversion and Additively Representable Set Rankings," Cahiers de recherche 16-2004, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, Fall.
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  12. 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.
  13. Bossert, Walter, 1997. "Uncertainty aversion in nonprobabilistic decision models," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 191-203, October.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer, vol. 41(2), pages 427-452, July.
  4. Mongin, Philippe & Pivato, Marcus, 2012. "Ranking Multidimensional Alternatives and Uncertain Prospects," MPRA Paper 42515, University Library of Munich, Germany.
  5. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
  6. Hill, Brian, 2012. "Unanimity and the aggregation of multiple prior opinions," Les Cahiers de Recherche 959, HEC Paris.

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