Bayesian group belief
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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.
I am very grateful for numerous helpful suggestions by a competent and diligent referee. This paper is based on my old unpublished paper ‘Opinion Pooling under Asymmetric Information,’ Public Economics 0407002, EconWPA, 2004. Meanwhile, interesting related results have been obtained independently by Marcus Pivato in hisworking paper ‘TheDiscursive Dilemma and Probabilistic Judgement Aggregation,’ MPRA Paper 8412, University Library of Munich, Germany, 2008.
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