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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 group members, who are themselves modelled as Bayesian agents and, crucially, may have different information. They may also have different prior beliefs and different domains (σ-algebras) on which they hold beliefs, to account for differences in awareness and conceptualisation. As is shown, group beliefs can incorporate all information spread across individuals without individuals having to communicate their information (which may be complex, hard-to-describe, or not describable in principle due to language restrictions); individuals should instead communicate their prior and posterior beliefs. 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), which contrast with familiar linear or geometric opinion pooling and the (Pareto) requirement of respecting unanimous beliefs.

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