巴西选票分布中的程式化事实
Stylized facts in Brazilian vote distributions
摘要：
选举，特别是在像巴西这样拥有1亿选民的国家，产生大规模的数据集，其中包含关于个人相互影响和作出选择的动态的宝贵信息。在这项工作中，我们进行了广泛的分析数据集可用于巴西比例选举的立法者和市议员在整个1970年至2012年期间，其中包括两个不同的政治制度：军事独裁和民主阶段。通过收到$v$选票的候选人数量的分布$P(v)$，我们对同一日历中的不同选举进行了比较分析，并作为时间的函数。分布$P(v)$呈现幂律指数$α$的无标度区，该指数不具有普适性，似乎是选民的特征。此外，我们观察到$α$通常随时间增加。我们提出了一个多物种模型，包括在一个系统的非线性微分方程的随机参数，允许理解的经验观察。我们的结论是，幂律指数$α$构成的选民互动的反馈程度的措施。了解人口的互动性，不仅与选举有关，因为在其他社会传染过程中也可能发生类似的反馈。
英文摘要：
Elections, specially in countries such as Brazil with an electorate of the order of 100 million people, yield large-scale data-sets embodying valuable information on the dynamics through which individuals influence each other and make choices. In this work we perform an extensive analysis of data sets available for Brazilian proportional elections of legislators and city councillors throughout the period 1970-2012, which embraces two distinct political regimes: a military dictatorship and a democratic phase. Through the distribution $P(v)$ of the number of candidates receiving $v$ votes, we perform a comparative analysis of different elections in the same calendar and as a function of time. The distributions $P(v)$ present a scale-free regime with a power-law exponent $α$ which is not universal and appears to be characteristic of the electorate. Moreover, we observe that $α$ typically increases with time. We propose a multi-species model consisting in a system of nonlinear differential equations with stochastic parameters that allows to understand the empirical observations. We conclude that the power-law exponent $α$ constitutes a measure of the degree of feedback of the electorate interactions. To know the interactivity of the population is relevant beyond the context of elections, since a similar feedback may occur in other social contagion processes.
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