Social Compass Model reveals how beliefs depolarize over time

A new paper by Corbit R. Sampson and Juan G. Restrepo from the University of Colorado Boulder brings mathematical rigor to understanding how polarized groups can depolarize over time. Their work on the Social Compass Model, published on arXiv, extends previous steady-state analyses by describing the full dynamics leading to consensus. Using the Ott-Antonsen Ansatz—a technique originally developed for coupled oscillators—they reduce the macroscopic opinion evolution to a finite set of ordinary differential equations. This allows them to analytically study the linear stability of polarized states and derive a dispersion relation for perturbation growth.

Crucially, the team discovered that the critical coupling strength required for depolarization depends solely on the first inverse moment of the conviction distribution across the population. However, the actual rate of depolarization is governed by higher moments of that distribution. This means two communities with identical thresholds for breaking polarization can take dramatically different times to reach consensus—differing by an order of magnitude. The framework also extends to networks with community structure, offering a path to model real-world social media polarization.