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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, TAU - Tel Aviv University)

  • 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," SciencePo Working papers Main hal-01024224, HAL.
    • Handle: RePEc:hal:spmain:hal-01024224
    DOI: 10.1016/j.jet.2011.06.018
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01024224
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    More about this item

    Keywords

    Aggregation of opinions; Ambiguity; Multiple priors;
    All these keywords.

    JEL classification:

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

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