Stylized Facts in Brazilian Vote Distributions

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 councilors throughout the period 1970–2014, which embraces two distinct political regimes: a military regime followed by a democratic one. We perform a comparative analysis of elections for legislative positions, in different states and years, through the distribution p(v) of the number of candidates receiving v votes. We show the impact of the different political regimes on the vote distributions. Although p(v) has a common shape, with a scaling behavior, quantitative details change over time and from one electorate to another. In order to interpret the observed features, we propose a multi-species model consisting in a system of nonlinear differential equations, with values of the parameters that reflect the heterogeneity of candidates. In its simplest setting, the model can not explain the cutoff, formed by the most voted candidates, whose success is determined mainly by their peculiar, intrinsic characteristics, such as previous publicity. However, the modeling allows to interpret the scaling of p(v), yielding a predictor of the degree of feedback in the interactions of the electorate. Knowledge of the feedback is relevant beyond the context of elections, since a similar interactivity may occur for other social contagion processes in the same population.