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arXiv · 0907.4818

Phase transition and information cascade in a voting model

Masato Hisakado·Shintaro Mori
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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.

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Masato Hisakado, Shintaro Mori. 2010-06-24. Phase transition and information cascade in a voting model. https://doi.org/10.1088/1751-8113%2F43%2F31%2F315207

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