投票模型中的相变和信息级联
Phase transition and information cascade in a voting model
摘要：
我们引入了一个类似于凯恩斯主义选美比赛的投票模型，并从数学的角度对其进行了分析。有两种选民模仿者和独立选民，还有两个候选人。我们的投票模型是一个二项分布（独立选民）掺杂在贝塔二项分布（模仿选民）。我们发现该系统的相变处于$t$的上限，其中$t$是时间（或投票数）。我们的模型包含三个阶段。如果模仿者占大多数，甚至占总选民的一半，投票率的收敛速度比二项分布要慢。如果无党派人士占选民的大多数，投票率的收敛速度与二项分布相同。我们还研究了为什么很难估计凯恩斯主义选美比赛的结论时，有一个信息级联。
英文摘要：
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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