Representing Aggregate Belief through the Competitive Equilibrium of a Securities Market

TL;DR

This paper introduces a market-based method for aggregating probabilistic beliefs of multiple agents by using securities market equilibrium, which naturally incorporates agent incentives and risk preferences.

Contribution

It develops a novel market-based framework for belief aggregation, linking equilibrium prices to consensus probabilities and addressing incentive compatibility.

Findings

Aggregate beliefs have desirable properties under constant risk aversion.

Market equilibrium prices reflect a consensus belief consistent with individual incentives.

The approach offers a decision-theoretic foundation for expert weighting in belief pooling.

Abstract

We consider the problem of belief aggregation: given a group of individual agents with probabilistic beliefs over a set of uncertain events, formulate a sensible consensus or aggregate probability distribution over these events. Researchers have proposed many aggregation methods, although on the question of which is best the general consensus is that there is no consensus. We develop a market-based approach to this problem, where agents bet on uncertain events by buying or selling securities contingent on their outcomes. Each agent acts in the market so as to maximize expected utility at given securities prices, limited in its activity only by its own risk aversion. The equilibrium prices of goods in this market represent aggregate beliefs. For agents with constant risk aversion, we demonstrate that the aggregate probability exhibits several desirable properties, and is related to independently motivated techniques. We argue that the market-based approach provides a plausible mechanism for belief aggregation in multiagent systems, as it directly addresses self-motivated agent incentives for participation and for truthfulness, and can provide a decision-theoretic foundation for the "expert weights" often employed in centralized pooling techniques.