ABSTRACT
We investigate the phenomena of political bi-polarization in a population of interacting agents by means of a generalized version of the model introduced by Vazquez et al. [Phys. Rev. E 101, 012101 (2020)] for the dynamics of voting intention. Each agent has a propensity p in [0,1] to vote for one of two political candidates. In an iteration step, two randomly chosen agents i and j with respective propensities pi and pj interact, and then pi either increases by an amount h>0 with a probability that is a nonlinear function of pi and pj or decreases by h with the complementary probability. We assume that each agent can interact with any other agent (all-to-all interactions). We study the behavior of the system under variations of a parameter q≥0 that measures the nonlinearity of the propensity update rule. We focus on the stability properties of the two distinct stationary states: mono-polarization in which all agents share the same extreme propensity (0 or 1), and bi-polarization where the population is divided into two groups with opposite and extreme propensities. We find that the bi-polarized state is stable for q