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Bayesian group belief

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  • Dietrich, Franz

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.

Suggested Citation

  • Dietrich, Franz, 2010. "Bayesian group belief," LSE Research Online Documents on Economics 29573, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:29573
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    File URL: http://eprints.lse.ac.uk/29573/
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    References listed on IDEAS

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    1. Franz Dietrich, 2004. "Opinion Pooling under Asymmetric Information," Public Economics 0407002, EconWPA.
    2. Dietrich Franz & List Christian, 2007. "Opinion pooling on general agendas," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Pivato, Marcus, 2008. "The Discursive Dilemma and Probabilistic Judgement Aggregation," MPRA Paper 8412, University Library of Munich, Germany.
    4. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
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    Citations

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    Cited by:

    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. 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.
    4. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    5. 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.
    6. Dietrich, Franz, 2016. "A Theory Of Bayesian Groups," MPRA Paper 75363, University Library of Munich, Germany.
    7. 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.
    8. 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.
    9. Dietrich Franz & List Christian, 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).
    10. Dietrich, Franz & List, Christian & Bradley, Richard, 2012. "A Joint Characterization of Belief Revision Rules," MPRA Paper 41240, University Library of Munich, Germany.

    More about this item

    Keywords

    utility-theory; aggregation; opinion pooling; Bayesianism; axiomatic approach; subjective probability; ISI;

    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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