Digital herders and phase transition in a voting model

In this paper, we discuss a voting model with two candidates, C 1 and C 2. We set two types of voters–herders and independents. The voting of independent voters is based on their fundamental values; on the other hand, the voting of herders is based on the number of votes. Herders always select the majority of the previous r votes, which is visible to them. We call them digital herders. We can accurately calculate the distribution of votes for special cases. When r ≥ 3, we find that a phase transition occurs at the upper limit of t, where t is the discrete time (or number of votes). As the fraction of herders increases, the model features a phase transition beyond which a state where most voters make the correct choice coexists with one where most of them are wrong. On the other hand, when r < 3, there is no 1 phase transition. In this case, the herders' performance is the same as that of the independent voters. Finally, we recognize the behavior of human beings by conducting simple experiments.