Dynamics of Confident Voting

TL;DR

This paper introduces the confident voter model, where voters have opinions and levels of confidence, analyzing how these dynamics influence consensus times and the formation of stripe states in different dimensions.

Contribution

The paper presents a novel confident voter model with two confidence levels, analyzing its dynamics and consensus times in mean-field and two-dimensional settings.

Findings

In mean-field, the population quickly reaches a mixed state before consensus.

Consensus times in two dimensions scale as N and N^{3/2}.

Stripe states with effective surface tension influence long-lived configurations.

Abstract

We introduce the confident voter model, in which each voter can be in one of two opinions and can additionally have two levels of commitment to an opinion --- confident and unsure. Upon interacting with an agent of a different opinion, a confident voter becomes less committed, or unsure, but does not change opinion. However, an unsure agent changes opinion by interacting with an agent of a different opinion. In the mean-field limit, a population of size N is quickly driven to a mixed state and remains close to this state before consensus is eventually achieved in a time of the order of ln N. In two dimensions, the distribution of consensus times is characterized by two distinct times --- one that scales linearly with N and another that appears to scale as N^{3/2}. The longer time arises from configurations that fall into long-lived states that consist of two (or more) single-opinion stripes before consensus is reached. These stripe states arise from an effective surface tension between domains of different opinions.