Aggregation of multiple prior opinions
AbstractExperts 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 InfoArticle provided by Elsevier in its journal Journal of Economic Theory.
Volume (Year): 146 (2011)
Issue (Month): 6 ()
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Web page: http://www.elsevier.com/locate/inca/622869
Aggregation of opinions; Ambiguity; Multiple priors;
Other versions of this item:
- D7 - Microeconomics - - Analysis of Collective Decision-Making
- D8 - Microeconomics - - Information, Knowledge, and Uncertainty
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- Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2008.
"Attitude toward imprecise information,"
UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers)
- Thibault Gajdos & Takashi Hayashi & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2006. "Attitude toward imprecise information," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00130179, HAL.
- 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).
- Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2008.
"Representation and aggregation of preferences under uncertainty,"
UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers)
- 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.
- Thibault Gajdos & Jean-Christophe Vergnaud, 2013.
"Decisions with conflicting and imprecise information,"
Social Choice and Welfare,
Springer, vol. 41(2), pages 427-452, July.
- Thibault Gajdos & Jean-Christophe Vergnaud, 2009. "Decisions with conflicting and imprecise information," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) hal-00443075, HAL.
- Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
- Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005.
"A Smooth Model of Decision Making under Ambiguity,"
Econometric Society, vol. 73(6), pages 1849-1892, November.
- Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
- 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.
- Chambers, Christopher & Takashi Hayashi, 2003.
"Preference Aggregation under Uncertainty: Savage vs. Pareto,"
1184, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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.
- 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.
- 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.
- Bossert, W., 1996.
"Uncertainty Aversion in Nonprobabilistic Decision Models,"
9609, University of Waterloo, Department of Economics.
- Bossert, Walter, 1997. "Uncertainty aversion in nonprobabilistic decision models," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 191-203, October.
- repec:hal:journl:halshs-00266049 is not listed on IDEAS
- Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, 09.
- Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2007.
"Probabilities in Economic Modeling,"
843644000000000357, UCLA Department of Economics.
- Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2008. "Probabilities in Economic Modelling," Levine's Working Paper Archive 122247000000001976, David K. Levine.
- 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.
- repec:hal:journl:halshs-00451982 is not listed on IDEAS
- Gilboa,Itzhak, 2009.
"Theory of Decision under Uncertainty,"
Cambridge University Press, number 9780521517324, October.
- 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.
- Itzhak Gilboa & Dov Samet & David Schmeidler, 2001.
"Utilitarian Aggregation of Beliefs and Tastes,"
Game Theory and Information
- Schmeidler, David, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Econometric Society, vol. 57(3), pages 571-87, May.
- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
- MONGIN, Philippe, 1993.
"Consistent Bayesian Aggregation,"
CORE Discussion Papers
1993019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
- 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.
- Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
- 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.
- F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
- 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.
- Hill, Brian, 2012. "Unanimity and the aggregation of multiple prior opinions," Les Cahiers de Recherche 959, HEC Paris.
- 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.
- 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.
- Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
- Mongin, Philippe & Pivato, Marcus, 2012. "Ranking Multidimensional Alternatives and Uncertain Prospects," MPRA Paper 42515, University Library of Munich, Germany.
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