On the Role of Zealotry in the Voter Model

TL;DR

This paper investigates how a finite number of unwavering zealots influence opinion dynamics in the voter model, revealing that even few zealots can prevent consensus and cause a Gaussian distribution of opinions.

Contribution

It introduces the analysis of zealots in the voter model across different dimensions, showing their significant impact on opinion distribution and consensus formation.

Findings

Zealots induce a Gaussian opinion distribution.

Number of zealots determines the opinion distribution width.

Few zealots can prevent consensus regardless of population size.

Abstract

We study the voter model with a finite density of zealots--voters than never change opinion. For equal numbers of zealots of each species, the distribution of magnetization (opinions) is Gaussian in the mean-field limit as well as in one and two dimensions, with a width that is proportional to 1/sqrt{Z}, where Z is the number of zealots, independent of the total number of voters. Thus just a few zealots can prevent consensus or even the formation of a robust majority.