Phase transition and information cascade in a voting model

TL;DR

This paper introduces a voting model with independent and copycat voters, revealing a phase transition at a critical point affecting convergence rates and explaining the difficulty in estimating outcomes during information cascades.

Contribution

It presents a mathematical analysis of a voting model with two voter types, identifying phase transitions and convergence behaviors, and explains challenges in outcome estimation during cascades.

Findings

Three distinct phases in voting dynamics.

Slower convergence when copycats dominate.

Difficulty in outcome estimation during information cascades.

Abstract

We introduce a voting model that is similar to a Keynesian beauty contest and analyze it from a mathematical point of view. There are two types of voters-copycat and independent-and two candidates. Our voting model is a binomial distribution (independent voters) doped in a beta binomial distribution (copycat voters). We find that the phase transition in this system is at the upper limit of $t$, where $t$ is the time (or the number of the votes). Our model contains three phases. If copycats constitute a majority or even half of the total voters, the voting rate converges more slowly than it would in a binomial distribution. If independents constitute the majority of voters, the voting rate converges at the same rate as it would in a binomial distribution. We also study why it is difficult to estimate the conclusion of a Keynesian beauty contest when there is an information cascade.