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Aggregation of multiple prior opinions

Author

Listed:
  • Hervé Crès

    () (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Itzhak Gilboa,

    (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)

  • Nicolas Vieille

    (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

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.

Suggested Citation

  • Hervé Crès & Itzhak Gilboa, & Nicolas Vieille, 2011. "Aggregation of multiple prior opinions," Post-Print hal-01024224, HAL.
  • Handle: RePEc:hal:journl:hal-01024224
    Note: View the original document on HAL open archive server: https://hal-sciencespo.archives-ouvertes.fr/hal-01024224
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Xiangyu Qu, 2017. "Separate aggregation of beliefs and values under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 503-519, February.
    2. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
    3. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2015. "Robust Social Decisions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01241819, HAL.
    4. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2014. "Aggregating Tastes, Beliefs, and Attitudes under Uncertainty," Post-Print halshs-01099032, HAL.
    5. Zuber, Stéphane, 2016. "Harsanyi’s theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 78-83.
    6. Stéphane Zuber, 2015. "Harsanyi's theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences," Post-Print halshs-01224145, HAL.
    7. Hill, Brian, 2012. "Unanimity and the aggregation of multiple prior opinions," HEC Research Papers Series 959, HEC Paris.
    8. Hill , Brian & Danan , Eric, 2014. "Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty," HEC Research Papers Series 1057, HEC Paris.
    9. repec:eee:reensy:v:188:y:2019:i:c:p:561-573 is not listed on IDEAS
    10. Marcello Basili, 2018. "Aggregation of experts’ opinions and conditional consensus opinion," Department of Economics University of Siena 780, Department of Economics, University of Siena.
    11. 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.
    12. repec:eee:corfin:v:45:y:2017:i:c:p:608-631 is not listed on IDEAS
    13. Mongin, Philippe & Pivato, Marcus, 2015. "Ranking multidimensional alternatives and uncertain prospects," Journal of Economic Theory, Elsevier, vol. 157(C), pages 146-171.
    14. Fleurbaey, Marc & Zuber, Stéphane, 2017. "Fair management of social risk," Journal of Economic Theory, Elsevier, vol. 169(C), pages 666-706.
    15. 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.
    16. Hannu Salonen, 2014. "Aggregating and Updating Information," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(2), pages 55-67, October.
    17. 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.
    18. 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.
    19. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers 1817, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    20. Berens, Stefan & Chochua, Lasha, 2017. "The impartial observer under uncertainty," Center for Mathematical Economics Working Papers 576, Center for Mathematical Economics, Bielefeld University.
    21. Pablo Amorós, 2017. "The problem of aggregating experts' opinions to select the winner of a competition," Working Papers 2017-04, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.

    More about this item

    Keywords

    Aggregation of opinions; Ambiguity; Multiple priors;

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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