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Fully Bayesian Aggregation

Author

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  • Franz Dietrich

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique)

Abstract

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only prefefence aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, and achieves only static rationality. Our characterisation of linear-geometric preference aggregation implies as corollaries a characterisation of linear value aggregation (Harsanyi's Theorem) and a characterisation of geometric belief aggregation.

Suggested Citation

  • Franz Dietrich, 2021. "Fully Bayesian Aggregation," Post-Print halshs-02905409, HAL.
    • Handle: RePEc:hal:journl:halshs-02905409
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02905409v3
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    References listed on IDEAS

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    Cited by:

    1. Brandl, Florian, 2021. "Belief-averaging and relative utilitarianism," Journal of Economic Theory, Elsevier, vol. 198(C).
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    3. Pivato, Marcus, 2022. "Bayesian social aggregation with accumulating evidence," Journal of Economic Theory, Elsevier, vol. 200(C).

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    More about this item

    Keywords

    expected-utility hypothesis; opinion pooling; static versus dynamic rationality; preference aggregation; ex-ante versus ex-port Pareto; rational group agent; uncertainty; spurious unanimity; Bayesianism; group rationality versus Praetianism;
    All these keywords.

    JEL classification:

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

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