Manipulation of Belief Aggregation Rules

TL;DR

This paper explores how belief aggregation rules can be manipulated in a setting where society reports probabilistic opinions to make collective portfolio decisions, linking equilibrium beliefs to market shares and characterizing implementable rules.

Contribution

It provides a novel characterization of Nash-implementable belief aggregation rules and links equilibrium beliefs to market shares in a portfolio choice context.

Findings

Belief reporting in Nash equilibrium corresponds to state-contingent wealth shares.

A necessary and sufficient condition for belief rule implementability is established.

The implementability condition is independent of risk attitudes.

Abstract

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.