An Equilibrium Approach to the Aggregation of Beliefs

Abstract

This paper presents a new answer to the old question of how to aggregate individual beliefs. We construct a model which allows agents to take arbitrage opportunities against the aggregated belief by making contingent claims against the states, and the aggregator (market maker) regulates the probability of states. When all claims from the agents are mutually covered for every realization of the state, an aggregation of individual beliefs is thus obtained. We prove the existence and uniqueness of the equilibrium aggregation, and also show that the aggregate belief lies in the convex hull of individual beliefs. This model allows us to address some important problems such as how individual agent’s attitude toward risk and wealth endowment affect the outcome of the aggregation process, and whether the aggregate belief satisfies the well-known properties like equal treatment.