Dynamics of Opinions with Social Biases

TL;DR

This paper analyzes how individual biases influence social opinion dynamics, revealing polarization effects and instability of interior equilibria across various network structures.

Contribution

It generalizes classical opinion dynamics models by incorporating biases, providing new insights into opinion polarization and stability analysis of equilibria.

Findings

Biases cause opinions to polarize towards interval boundaries.

Interior equilibria are generally unstable across network structures.

Interval centroid remains unstable regardless of biases and network topology.

Abstract

This paper aims to provide a systemic analysis to social opinion dynamics subject to individual biases. As a generalization of the classical DeGroot social interactions, defined by linearly coupled dynamics of peer opinions that evolve over time, biases add to state-dependent edge weights and therefore lead to highly nonlinear network dynamics. Previous studies have dealt with convergence and stability analysis of such systems for a few specific initial node opinions and network structures, and here we focus on how individual biases affect social equilibria and their stabilities. First of all, we prove that when the initial network opinions are polarized towards one side of the state space, node biases will drive the opinion evolution to the corresponding interval boundaries. Such polarization attraction effect continues to hold under even directed and switching network structures. Next, for a few fundamental network structures, some important interior network equilibria are presented explicitly for a wide range of system parameters, which are shown to be locally unstable in general. Particularly, the interval centroid is proven to be unstable regardless of the bias level and the network topologies.