Model of binary opinion dynamics: Coarsening and effect of disorder

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 θ ≃ 0.235 and dynamic exponent z ≃ 1.02 ± 0.02. Introducing disorder through a parameter called rigidity coefficient ρ (probability that people are completely rigid and never change their opinion), the transition to a heterogeneous society at ρ = 0 + is obtained. Close to ρ = 0, the equilibrium values of the dynamic variables show power law scaling behaviour with ρ. We also discuss the effect of having both quenched and annealed disorder in the system.

Minority-spin dynamics in the nonhomogeneous Ising model: Diverging time scales and exponents

“…Different ways of employing the zero temperature quench have also been explored in some very recent works in the Ising model [14][15][16]. Models with more complicated interactions with binary spin variables have often indicated the existence of dynamical universality classes other than the simple Ising model even in one dimension [17].…”

Phase transitions in a two-parameter model of opinion dynamics with random kinetic exchanges

“…The evolution usually leads to a steady state characterised either by a homogeneous state where people have similar opinion or a heterogeneous behaviour where people have widely different opinions. The interactions of the individuals in opinion dynamics models can be studied in terms of appropriate tunable parameters and it is of interest to observe whether such parameters can drive a phase transition in the system [6][7][8][9][10].…”

“…The evolution usually leads to a steady state characterised either by a homogeneous state where people have similar opinion or a heterogeneous behaviour where people have widely different opinions. The interactions of the individuals in opinion dynamics models can be studied in terms of appropriate tunable parameters and it is of interest to observe whether such parameters can drive a phase transition in the system [6][7][8][9][10].While several different schemes have been proposed for possible evolution of opinions, a number of models have adopted the idea of kinetic exchanges in opinion formation [10][11][12][13][14]. In one such recently introduced model [10], the opinions of individuals, continuously varying from -1 to +1, were assumed to change after pairwise interactions.…”

An Energy-Based Interaction Model for Population Opinion Dynamics with Topic Coupling

“…The generalized version of these games can be split into two categories. A binary (or more generally, discrete) opinion model [10,14,21,22,31,41,42] requires agents to negotiate an opinion on a topic that has two possibilities and therefore, the final state of the system divides agents into two distinct groups, see [40], [5]. The alternative is a system in which the opinion space is continuous [8,15,23,44].…”