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Fully Bayesian Aggregation

Author

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  • Franz Dietrich

    (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, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - 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 preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but achieves only static rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs.

Suggested Citation

  • Franz Dietrich, 2021. "Fully Bayesian Aggregation," Post-Print hal-03194928, HAL.
    • Handle: RePEc:hal:journl:hal-03194928
    DOI: 10.1016/j.jet.2021.105255
    Note: View the original document on HAL open archive server: https://hal.science/hal-03194928
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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).
    2. Lorenzo Bastianello & José Heleno Faro & Ana Santos, 2022. "Dynamically consistent objective and subjective rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 477-504, September.
    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

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

    JEL classification:

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

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