Voter models with contrarian agents

TL;DR

This paper explores how contrarian agents influence opinion dynamics in voter models, showing that even few contrarians prevent consensus and significantly affect fluctuations depending on their behavior.

Contribution

It introduces three linear extensions of the voter model with contrarians, analyzing their impact on consensus and opinion distribution.

Findings

Contrarians prevent consensus in all models.

Fluctuations are larger in model 2 with rare contrarians.

Equilibrium distributions are derived using van Kampen and Fokker-Planck methods.

Abstract

In the voter and many other opinion formation models, agents are assumed to behave as congregators (also called the conformists); they are attracted to the opinions of others. In this study, I investigate linear extensions of the voter model with contrarian agents. An agent is either congregator or contrarian and assumes a binary opinion. I investigate three models that differ in the behavior of the contrarian toward other agents. In model 1, contrarians mimic the opinions of other contrarians and oppose (i.e., try to select the opinion opposite to) those of congregators. In model 2, contrarians mimic the opinions of congregators and oppose those of other contrarians. In model 3, contrarians oppose anybody. In all models, congregators are assumed to like anybody. I show that even a small number of contrarians prohibits the consensus in the entire population to be reached in all three models. I also obtain the equilibrium distributions using the van Kampen small-fluctuation approximation and the Fokker-Planck equation for the case of many contrarians and a single contrarian, respectively. I show that the fluctuation around the symmetric coexistence equilibrium is much larger in model 2 than in models 1 and 3 when contrarians are rare.