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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 - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - 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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03194928, HAL.
  • Handle: RePEc:hal:cesptp:hal-03194928
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-03194928
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    References listed on IDEAS

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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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