Combining Overlapping Information

A decision maker trying to learn about an uncertain quantity may obtain divergent information from a number of sources (e.g., experts). In this paper we study the decision maker's problem of aggregating this information to form his posterior distribution when he believes that the experts' opinions are dependent due to shared information. Examples in both normal and Bernoulli frameworks lead to some surprising general insights regarding the impact of the dependence on the posterior distribution. The study has implications for practitioners who face real-world information-aggregation problems and for groups of experts who seek a consensus.