Opinion dynamics in two dimensions: domain coarsening leads to stable bi-polarization and anomalous scaling exponents

Abstract

We study an opinion dynamics model that explores the competition between persuasion and compromise in a population of agents with nearest-neighbor interactions on a two-dimensional square lattice. Each agent can hold either a positive or a negative opinion orientation, and can have two levels of intensity?moderate and extremist. When two interacting agents have the same orientation they become extremists with persuasion probability p, while if they have opposite orientations they become moderate with compromise probability q. These updating rules lead to the formation of same-opinion domains with a coarsening dynamics that depends on the ratio r = p/q. The population initially evolves to a centralized state for small r, where domains are composed of moderate agents and coarsening is without surface tension, and to a bi-polarized state for large r, where domains are formed by extremist agents and coarsening is driven by curvature. Consensus in an extreme opinion is finally reached in a time that scales with the population size N and r as for small r and as for large r. Bi-polarization could be quite stable when the system falls into a striped state where agents organize into single-opinion horizontal, vertical or diagonal bands. An analysis of the stripe dynamics towards consensus allows us to obtain an approximate expression for τ, which shows that the exponent 1.64 is a result of the diffusion of the stripe interfaces combined with their roughness properties.