Consensus versus persistence of disagreement in opinion formation: the role of zealots

TL;DR

This paper explores how the presence of unwavering zealots influences opinion dynamics in a three-state model, revealing diverse collective behaviors and phase transitions depending on zealot density and interaction rules.

Contribution

It introduces a comprehensive analysis of opinion formation with zealots, identifying four distinct collective regimes and calculating critical zealot densities for opinion diversity.

Findings

High zealot density leads to consensus on their opinion.

Low zealot density allows dissenters to survive or require a critical mass.

Transitions between regimes can be smooth or abrupt with hysteresis effects.

Abstract

We consider a general class of three--state models where individuals hold one of two opposite opinions, or are neutral, and exchange opinions in generic pairwise interactions. We show that when opinions spread in a population where a fraction of individuals (zealots) maintain unshakably their opinion, one of four qualitatively distinct kinds of collective dynamics arise, depending on the specific rules governing the social interactions. Unsurprisingly, when their density is high, zealots drive the whole population to consensus on their opinion. For low densities a rich phase diagram emerges: a finite population of dissenters can survive and be the only stationary state or may need a critical mass or dissenters to be sustained; the critical mass may vanish or not as the density is reduced; the transition to the high density regime can be smooth or abrupt, and shows interesting hysteretic effects. For each choice of the interaction rules we calculate the critical density of zealots above which diverse opinions cannot survive.