Opinion Pooling under Asymmetric Information

If each member of a group assigns a certain probability to a hypothesis, what probability should the collective as a whole assign? More generally, how should individual probability functions be merged into a single collective one? I investigate this question in case that the individual probability functions are based on different information sets. Under suitable assumptions, I present a simple solution to this aggregation problem, and a more complex solution that can cope with any overlaps between different persons' information sets. The solutions are derived from an axiomatic system that models the individuals as well as the collective as Bayesian rational agents. Two notable features are that the solutions may be parameter-free, and that they incorporate each individual's information although the individuals need not communicate their (perhaps very complex) information, but rather reveal only the resulting probabilities.