Bayesian Group Agents and Two Modes of Aggregation

Suppose we have a group of Bayesian agents, and suppose that they would like for their group as a whole to be a Bayesian agent as well. Moreover, suppose that those agents want the probabilities and utilities attached to this group agent to be aggregated from the individual probabilities and utilities in reasonable ways. Two ways of aggregating their individual data are available to them, viz., ex ante aggregation and ex post aggregation. The former aggregates expected utilities directly, whereas the latter aggregates probabilities and utilities separately. A number of recent formal results show that both approaches have problematic implications. This study discusses the philosophical issues arising from those results. In this process, I hope to convince the reader that these results about Bayesian aggregation are highly significant to decision theorists, but also of immense interest to theorists working in areas such as ethics and political philosophy.