Marginalization and Linear Opinion Pools

Abstract

Abstract Suppose a decision maker has asked a group of experts to assess subjective probability distributions over some space, and he wishes to find a consensus probability distribution as a function of these. The assumption that finding the consensus distribution commutes with marginalization of the distributions implies that the consensus must be found using a linear opinion pool (weighted average), provided the space being considered contains three or more points. Some of the consequences of this result are discussed.