Probabilistic Opinion Pooling

Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This chapter is a review of several proposed solutions to this problem, focusing on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). Axiomatic characterizations of each class of pooling functions are presented (most characterizations are classic results, but one is new), with the argument that linear pooling can be justified “procedurally” but not “epistemically”, while the other two pooling methods can be justified “epistemically”. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. In conclusion a number of other pooling methods are mentioned.