Dynamics of Confident Voting

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.Comment: 13 pages, 8 figures, iop format. Version 2 has minor revisions in response to referee comments. For publication in JSTA