Role of conviction in nonequilibrium models of opinion formation

TL;DR

This paper investigates how disorder and conviction influence phase transitions in a class of discrete opinion models, revealing the effects of interaction types, update schemes, and disorder on collective opinion formation.

Contribution

It introduces a mean-field model with disorder in agent interactions and convictions, analyzing how these factors affect critical behavior and phase transitions in opinion dynamics.

Findings

A non-equilibrium phase transition occurs at a critical probability p_c.

The critical line is affected by the type of disorder and update scheme.

Disorder can spoil the transition under certain conditions.

Abstract

We analyze the critical behavior of a class of discrete opinion models in the presence of disorder. Within this class, each agent opinion takes a discrete value ($\pm 1$ or 0) and its time evolution is ruled by two terms, one representing agent-agent interactions and the other the degree of conviction or persuasion (a self-interaction). The mean-field limit, where each agent can interact evenly with any other, is considered. Disorder is introduced in the strength of both interactions, with either quenched or annealed random variables. With probability $p$ (1-$p$), a pairwise interaction reflects a negative (positive) coupling, while the degree of conviction also follows a binary probability distribution (two different discrete probability distributions are considered). Numerical simulations show that a non-equilibrium continuous phase transition, from a disordered state to a state with a prevailing opinion, occurs at a critical point $p_{c}$ that depends on the distribution of the convictions, the transition being spoiled in some cases. We also show how the critical line, for each model, is affected by the update scheme (either parallel or sequential) as well as by the kind of disorder (either quenched or annealed).