Shifting consensus in a biased compromise model

TL;DR

This paper studies how bias influences political party formation and dynamics within a bounded confidence model, revealing how weak bias shifts opinions and how strong bias can cause parties to drift and dissolve.

Contribution

It introduces a nonlinear bias model with self-incitement, applying advanced mathematical techniques to analyze party drift and dissolution thresholds.

Findings

Weak bias shifts average opinions and reduces party sizes.

Strong bias causes parties to drift and eventually dissolve.

Mathematical analysis quantifies drift speeds and thresholds.

Abstract

We investigate the effect of bias on the formation and dynamics of political parties in the bounded confidence model. For weak bias, we quantify the change in average opinion and potential dispersion and decrease in party size. For nonlinear bias modeling self-incitement, we establish coherent drifting motion of parties on a background of uniform opinion distribution for biases below a critical threshold where parties dissolve. Technically, we use geometric singular perturbation theory to derive drift speeds, we rely on a nonlocal center manifold analysis to construct drifting parties near threshold, and we implement numerical continuation in a forward-backward delay equation to connect asymptotic regimes.