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A theory of Bayesian groups

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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

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated "Groupthink", Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non‐public or even private information (learnt by not all or just one individual), or to non‐representable information (not representable by any event in the domain where credences are held). I propose a taxonomy of six types of ‘group Bayesianism'. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non‐representable information, etc. Six corresponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.'s central result (with minor corrections). Another theorem—that for public non‐representable information—fills a gap in the theory of externally Bayesian opinion pooling.

Suggested Citation

  • Franz Dietrich, 2019. "A theory of Bayesian groups," Post-Print halshs-01744083, HAL.
  • Handle: RePEc:hal:journl:halshs-01744083
    DOI: 10.1111/nous.12233
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    References listed on IDEAS

    as
    1. Franz Dietrich, 2010. "Bayesian group belief," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 595-626, October.
    2. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    3. Peter A. Morris, 1974. "Decision Analysis Expert Use," Management Science, INFORMS, vol. 20(9), pages 1233-1241, May.
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    Cited by:

    1. Ding, Huihui & Pivato, Marcus, 2021. "Deliberation and epistemic democracy," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 138-167.
    2. Franz Dietrich & Christian List, 2017. "Probabilistic opinion pooling generalized. Part two: the premise-based approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 787-814, April.
    3. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    4. Christian J. Feldbacher-Escamilla & Gerhard Schurz, 2023. "Meta-Inductive Probability Aggregation," Theory and Decision, Springer, vol. 95(4), pages 663-689, November.
    5. Franz Dietrich & Christian List, 2021. "Dynamically rational judgment aggregation," Post-Print halshs-03140090, HAL.

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    More about this item

    JEL classification:

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

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