A new model of binary opinion dynamics: coarsening and effect of disorder

TL;DR

This paper introduces a binary opinion model where individuals adopt neighboring opinions based on domain size, revealing novel scaling behaviors and a disorder-induced transition to heterogeneity, with implications for understanding social dynamics.

Contribution

The paper presents a new opinion dynamics model incorporating domain size influence and disorder effects, highlighting unique scaling laws and phase transition behavior.

Findings

System evolves to homogeneous state from random initial conditions.

Novel scaling exponents: persistence $ heta \,\simeq\, 0.235$, dynamic $z \,\simeq\, 1.02$.

Disorder induces a transition to heterogeneity at $ ho=0^{+}$.

Abstract

We propose a model of binary opinion in which the opinion of the individuals change according to the state of their neighbouring domains. If the neighbouring domains have opposite opinions, then the opinion of the domain with the larger size is followed. Starting from a random configuration, the system evolves to a homogeneous state. The dynamical evolution show novel scaling behaviour with the persistence exponent $\theta \simeq 0.235$ and dynamic exponent $z \simeq1.02 \pm 0.02$. Introducing disorder through a parameter called rigidity coefficient $\rho$ (probability that people are completely rigid and never change their opinion), the transition to a heterogeneous society at $\rho = 0^{+}$ is obtained. Close to $\rho =0$, the equilibrium values of the dynamic variables show power law scaling behaviour with $\rho$. We also discuss the effect of having both quenched and annealed disorder in the system.