Collective group drift in a PDE-based opinion dynamics model with biased perception kernels

TL;DR

This paper models opinion dynamics using a PDE with biased perception kernels, revealing how bias leads to group polarization and collective drift towards extremities, with stability analysis and numerical simulations supporting these findings.

Contribution

Introduces a new PDE model with biased perception kernels to analyze how bias influences opinion group formation and polarization dynamics.

Findings

Biased populations can form opinionated groups despite bias.

Excessive bias stabilizes the homogeneous mixed state, preventing consensus.

Groups tend to drift towards extremes over time due to bias.

Abstract

In the age of technology, individuals accelerate their biased gathering of information which in turn leads to a population becoming extreme and more polarized. Here we study a partial differential equation model for opinion dynamics that exhibits collective behavior subject to nonlocal interactions. We developed a new interaction kernel function to represent biased information gathering. Through a linear stability analysis, we show that biased populations can still form opinionated groups. However, a population that is too heavily biased can no longer come to a consensus, that is, the initial homogeneous mixed state becomes stable. Numerical simulations with biased information gathering show the ability for groups to collectively drift towards one end of the opinion space. This means that a small bias in each individual will collectively lead to groups of individuals becoming extreme together. The characteristic time scale for a groups existence is captured from numerical experiments using the temporal correlation function. Supplementing this, we included a measure of how different each population is after regular time intervals using a form of the Manhattan and Euclidean distance metrics. We conclude by exploring how wall boundary conditions induce pattern formation initially on the most extreme sides of the domain.