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Bayesian group belief

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Abstract

If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of the group members. The group members may have different information, different prior beliefs and even different domains (algebras) within which they hold beliefs, accounting for differences in awareness and conceptualisation. As is shown, group beliefs can incorporate all information spread across individuals without individuals having to explicitly communicate their information (that may be too complex or personal to describe, or not describable in principle in the language). The group beliefs derived here take a simple multiplicative form if people's information is independent (and a more complex form if information overlaps arbitrarily). This form contrasts with familiar linear or geometric opinion pooling and the (Pareto) requirement of respecting unanimous beliefs.
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  • 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.
    • Handle: RePEc:spr:sochwe:v:35:y:2010:i:4:p:595-626
    DOI: 10.1007/s00355-010-0453-x
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    1. Dietrich, F.K. & List, C., 2007. "Opinion pooling on general agendas"," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    3. Mark J. Schervish & Teddy Seidenfeld & Joseph B. Kadane, 1991. "Shared Preferences and State-Dependent Utilities," Management Science, INFORMS, vol. 37(12), pages 1575-1589, December.
    4. Franz Dietrich, 2004. "Opinion Pooling under Asymmetric Information," Public Economics 0407002, University Library of Munich, Germany.
    5. Peter A. Morris, 1974. "Decision Analysis Expert Use," Management Science, INFORMS, vol. 20(9), pages 1233-1241, May.
    6. Pivato, Marcus, 2008. "The Discursive Dilemma and Probabilistic Judgement Aggregation," MPRA Paper 8412, University Library of Munich, Germany.
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    1. Franz Dietrich & Christian List, 2017. "Probabilistic opinion pooling generalized. Part one: general agendas," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 747-786, April.
    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 & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    4. Elena M. Parilina & Georges Zaccour, 2022. "Sustainable Cooperation in Dynamic Games on Event Trees with Players’ Asymmetric Beliefs," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 92-120, July.
    5. List, Christian, 2010. "The theory of judgment aggregation: an introductory review," LSE Research Online Documents on Economics 27596, London School of Economics and Political Science, LSE Library.
    6. Franz Dietrich & Christian List, 2021. "Dynamically rational judgment aggregation," Post-Print halshs-03140090, HAL.
    7. Francesco Billari & Rebecca Graziani & Eugenio Melilli, 2014. "Stochastic Population Forecasting Based on Combinations of Expert Evaluations Within the Bayesian Paradigm," Demography, Springer;Population Association of America (PAA), vol. 51(5), pages 1933-1954, October.
    8. Philip E. Tetlock & Christopher Karvetski & Ville A. Satopää & Kevin Chen, 2024. "Long‐range subjective‐probability forecasts of slow‐motion variables in world politics: Exploring limits on expert judgment," Futures & Foresight Science, John Wiley & Sons, vol. 6(1), March.
    9. Dietrich, Franz, 2016. "A Theory Of Bayesian Groups," MPRA Paper 75363, University Library of Munich, Germany.
    10. Ruth Ben-Yashar & Leif Danziger, 2015. "When is voting optimal?," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 341-356, October.
    11. Ding, Huihui & Pivato, Marcus, 2021. "Deliberation and epistemic democracy," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 138-167.
    12. Satopää, Ville A. & Salikhov, Marat & Tetlock, Philip E. & Mellers, Barbara, 2023. "Decomposing the effects of crowd-wisdom aggregators: The bias–information–noise (BIN) model," International Journal of Forecasting, Elsevier, vol. 39(1), pages 470-485.
    13. Aurélien Baillon & Laure Cabantous & Peter Wakker, 2012. "Aggregating imprecise or conflicting beliefs: An experimental investigation using modern ambiguity theories," Journal of Risk and Uncertainty, Springer, vol. 44(2), pages 115-147, April.
    14. Dietrich, F.K. & List, C., 2008. "The aggregation of propositional attitudes: towards a general theory," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    15. Dietrich, Franz & List, Christian & Bradley, Richard, 2012. "A Joint Characterization of Belief Revision Rules," MPRA Paper 41240, University Library of Munich, Germany.

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    More about this item

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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