MAXIMUM-ENTROPY AGGREGATION OF EXPERT PREDICTIONS

This paper presents a maximum entropy framework for the aggregation of expert opinions where the expert opinions concern the prediction of t he outcome of an uncertain event. The event to be predicted and indivi dual predictions rendered are assumed to be discrete random variables. A measure of expert competence is defined using a distance metric bet ween the actual outcome of the event and each expert's predicted outco me. Following Levy and Delic (1994), we use Shannon's information meas ure (Shannon 1948, Jaynes 1957) to derive aggregation rules for combin ing two or more expert predictions into a single aggregated prediction that appropriately calibrates different degrees of expert competence and reflects any dependence that may exist among the expert prediction s. The resulting maximum entropy aggregated prediction is least prejud iced in the sense that it utilizes all information available but remai ns maximally noncommittal with regard to information not available. Nu merical examples to illuminate the implications of maximum entropy agg regation are also presented.