A Multi-Agent Model for Polarization under Confirmation Bias in Social Networks

TL;DR

This paper introduces a multi-agent model for social polarization influenced by confirmation bias, analyzing how network structure affects whether polarization persists or vanishes, with insights into influence dynamics and convergence behavior.

Contribution

The paper extends the DeGroot social learning model by incorporating confirmation bias and provides conditions under which polarization persists or diminishes in different network structures.

Findings

Polarization converges to zero in strongly-connected influence graphs.

In symmetric circulation graphs, all agents converge to a unique belief.

Polarization may persist in weakly-connected graphs under confirmation bias.

Abstract

We describe a model for polarization in multi-agent systems based on Esteban and Ray's standard measure of polarization from economics. Agents evolve by updating their beliefs (opinions) based on an underlying influence graph, as in the standard DeGroot model for social learning, but under a confirmation bias; i.e., a discounting of opinions of agents with dissimilar views. We show that even under this bias polarization eventually vanishes (converges to zero) if the influence graph is strongly-connected. If the influence graph is a regular symmetric circulation, we determine the unique belief value to which all agents converge. Our more insightful result establishes that, under some natural assumptions, if polarization does not eventually vanish then either there is a disconnected subgroup of agents, or some agent influences others more than she is influenced. We also show that polarization does not necessarily vanish in weakly-connected graphs under confirmation bias. We illustrate our model with a series of case studies and simulations, and show how it relates to the classic DeGroot model for social learning.