Belief Identification in Populations

2026-07-18

AI Summary

This study investigates the identifiability of individual prior belief distributions from aggregated beliefs of an anonymous population over a set of binary events. Focusing on populations composed of Bayesian agents, the authors uncover a fundamental connection between belief identifiability and the graph structure induced by the event family on the state space: prior distributions are typically identifiable when the induced graph is non-separable, but generally unidentifiable under separable graphs. By integrating Bayesian inference, identification theory for probability distributions, and graph-theoretic separability analysis, the paper establishes theoretical limits on recovering belief heterogeneity from aggregate data and introduces a graph-based criterion for identifiability, offering clear guidance for experimental design and mechanism construction.

Abstract

We study the identification of belief distributions in a population of Bayesian agents from anonymous aggregate belief data. While a single Bayesian agent's full belief can be recovered from beliefs over a suitable collection of binary events, this principle need not extend to populations: event-by-event distributions of beliefs may fail to identify the underlying distribution of priors. We study when this failure is generic and when it is exceptional. Identification is governed by the graph-theoretic structure induced by the observed family of events on the state space. Among $n$-agent distributions, identification is generic if the induced graph is nonseparable, while non-identification is generic if the graph is separable. The results establish both limits and design principles for recovering belief heterogeneity from aggregate belief data.

Problem

• belief identification
• Bayesian agents
• aggregate belief data
• prior distribution
• population heterogeneity

Innovation

• belief identification
• Bayesian agents
• aggregate data
• graph separability
• heterogeneous priors