Dynamics of Vacillating Voters

TL;DR

The paper introduces a vacillating voter model where voters consult two neighbors and tend toward a neutral state, leading to unique domain growth and exponential consensus times.

Contribution

It presents a new voter model with vacillation behavior, revealing anti-coarsening dynamics and exponential scaling of consensus time in higher dimensions.

Findings

Minority domains grow as t^{1/(d+1)} in spatial dimensions d>1

Time to reach consensus scales exponentially with the number of voters

Global bias toward zero magnetization influences domain dynamics

Abstract

We introduce the vacillating voter model in which each voter consults two neighbors to decide its state, and changes opinion if it disagrees with either neighbor. This irresolution leads to a global bias toward zero magnetization. In spatial dimension d>1, anti-coarsening arises in which the linear dimension L of minority domains grows as t^{1/(d+1)}. One consequence is that the time to reach consensus scales exponentially with the number of voters.