Opinion pooling under informational asymmetries

Abstract
If a group as a whole 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, possibly with di¤erent priors and di¤erent information. Group beliefs are shown to take a simple multiplicative form if people’s information is independent, and a more complex form if information can overlap arbitrarily. This shows that group beliefs can incorporate all information spread over the individuals without the individuals having to communicate their (possibly complex and hard-to-describe) private information; communicating prior and posterior beliefs su¢ ces.
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