Combining Expert Judgments: A Bayesian Approach

This paper presents a new approach to the problem of expert resolution. The proposed analytic structure provides a mechanism by which a decision maker can incorporate the possibly conflicting probability assessments of a group of experts. The approach is based upon the Bayesian inferential framework presented in Morris, P. A. 1974. Decision analysis expert use. Management Sci. 20 (9, May). A number of specific results are derived from analysis of a generic model structure. In the single expert continuous variable case, we prove that the decision maker should process a calibrated expert's opinion by multiplying the expert's probability assessment by his own prior probability assessment and normalizing. A method for subjectively calibrating an expert is also presented. In the multi-expert case, we obtain a simple multiplicative rule for combining the expert judgments. We also prove the existence of a composite probability function which measures the joint information contained in the probability assessments generated by a panel of experts. The interesting result is that composite prior should be processed as if it were the probability statement of a single calibrated expert.