Manipulation of Belief Aggregation Rules

This paper studies manipulation of belief aggregation rules in the setting where the society first collects individual's probabilistic opinions and then solves a public portfolio choice problem with common utility based on the aggregate belief. First, we show that belief reporting in Nash equilibrium under the linear opinion pool and log utility is identified as the profile of state-contingent wealth shares in parimutuel equilibrium with risk-neutral preference. Then we characterize belief aggregation rules which are Nash-implementable. We provide a necessary and essentially sufficient condition for implementability, which is independent of the common risk attitude.