A Formal Model for Polarization under Confirmation Bias in Social Networks

TL;DR

This paper introduces a formal model for social polarization influenced by confirmation bias, analyzing how network structure affects whether polarization persists or vanishes, with implications for understanding social dynamics.

Contribution

It extends the DeGroot model by incorporating confirmation bias and provides conditions under which polarization persists or diminishes in social networks.

Findings

Polarization vanishes in strongly-connected influence graphs.

In regular symmetric circulation graphs, 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 family of polarization measures 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 prove that polarization does not necessarily vanish in weakly-connected graphs under confirmation bias. Furthermore, we show how our model relates to the classic DeGroot model for social learning. We illustrate our model with several simulations of a running example about polarization over vaccines and of other case studies. The theoretical results and simulations will provide insight into the phenomenon of polarization.