Dynamics of Confident Voting

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.