Low-dimensional Dynamics of the Social Compass Model

2026-06-24

AI Summary

This study investigates the dynamic mechanisms underlying the transition from polarized to depolarized states in the social compass model. By employing the Ott–Antonsen reduction method, the high-dimensional macroscopic dynamics are reduced to a finite-dimensional system of ordinary differential equations, yielding the first low-dimensional descriptive framework for dynamic depolarization in this model. Theoretical analysis reveals that the critical coupling strength depends solely on the first inverse moment of the belief distribution, while the depolarization rate is governed by higher-order moments; notably, distinct belief distributions can exhibit markedly different depolarization timescales even at identical critical coupling strengths. The framework is further extended to networks with community structure, and the evolution of perturbations around polarized states is characterized through dispersion relations.

Abstract

The social compass model has been recently proposed as a model for depolarization in populations where individuals have multiple, possibly correlated, opinions. Previous work has focused on the steady state of this model, but has not addressed the dynamics leading to depolarization. We show that the macroscopic dynamics of the social compass model can be described using the Ott-Antonsen Ansatz and that, for initially clustered opinions, the resulting equations reduce to a finite-dimensional system of ordinary differential equations. We study the linear stability of the polarized state and find a dispersion relation for the growth rate of perturbations from this state. We find that the critical coupling for depolarization depends only on the first inverse moment of the conviction distribution, whereas the rate of depolarization depends on higher moments. Consequently, conviction distributions with the same critical coupling can exhibit vastly different depolarization timescales. We also demonstrate how our analysis can be extended to study depolarization in the presence of community structure.

Problem

• depolarization
• social compass model
• low-dimensional dynamics
• opinion dynamics
• conviction distribution

Innovation

• Ott-Antonsen Ansatz
• depolarization dynamics
• social compass model
• finite-dimensional reduction
• conviction distribution moments