Dynamics of opinion polarization in a population

Abstract

This article addresses the polarization of the population around an idea and proposes a simple model that describes its dynamics in a society characterized by asymmetries in freedom of expression. The model considers a population divided into followers of an idea, consisting of moderate sympathizers and staunch defenders, and a group of opponents who try to spread their position but are also susceptible to opinion change. An analysis of stability of the proposed system of differential equations is conducted to examine policies that prevent homogenization around the idea. The results reveal conditionally stable equilibrium points that represent the coexistence of opinions and the extinction of polarization. Two threshold values are proposed to determine the persistence of polarization over time. Furthermore, the results of the model are validated through the analysis of two real cases of polarization in Colombian society, demonstrating its ability to reproduce the general behavior of opinion divergence and its utility in polarization control.