Digital herders and phase transition in a voting model

TL;DR

This paper models a voting system with herders and independents, revealing a phase transition phenomenon when herders base their votes on the last r votes, which impacts the collective decision accuracy.

Contribution

It introduces a voting model with digital herders and identifies a phase transition at r>=3, providing insights into collective decision dynamics and human voting behavior.

Findings

Phase transition occurs at r>=3 with increasing herders.

Herders' influence causes coexistence of correct and incorrect majority states.

Experimental results support the model's behavioral assumptions.

Abstract

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 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.