Revealed Social Networks

2025-01-05

AI Summary

This paper addresses the identifiability of Linear-in-Means (LIM) models: while unidimensional outcomes typically yield non-identifiable models, multidimensional outcomes enable generic identification under natural conditions—such as cross-dimensional heterogeneity in peer effects and exogenous variation in participation rates. The study develops the first theoretical framework for identifying latent social networks from individual choice data alone, without observing network structure—jointly identifying both the adjacency matrix and social influence coefficients. Methodologically, it integrates structural identification theory, revealed preference tests, and exogenous variation analysis; under sufficient participation variation, it ensures unique identification and provides a testable framework for cross-population network extrapolation and model validation. The core contribution is a paradigm shift away from reliance on observed network data, establishing a robust identification foundation for LIM models in multidimensional settings.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Application Domains: Humanities & Computational Social Science
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Social Networks and Social Media: Social media analysis through the lenses of networks
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

People are influenced by their peers when making decisions. In this paper, we study the linear-in-means model which is the standard empirical model of peer effects. As data on the underlying social network is often difficult to come by, we focus on data that only captures an agent's choices. Under exogenous agent participation variation, we study two questions. We first develop a revealed preference style test for the linear-in-means model. We then study the identification properties of the linear-in-means model. With sufficient participation variation, we show how an analyst is able to recover the underlying network structure and social influence parameters from choice data. Our identification result holds when we allow the social network to vary across contexts. To recover predictive power, we consider a refinement which allows us to extrapolate the underlying network structure across groups and provide a test of this version of the model.

Problem

• Tests linear-in-means model using revealed preference
• Examines identifiability based on outcome variable dimension
• Links multi-dimensional outcomes to generic identification conditions

Innovation

• Revealed preference test for peer effects
• Linear program with incentive compatibility
• Multi-dimensional outcome ensures identifiability