Unraveling people interactivity by means of electoral vote

Elections embody valuable information on the dynamics through
which individuals influence each other and make choices.
We analyze proportional elections in Brazil, a country with a diversified and huge
electorate of around 100 million people, covering the period 1970-2012,
which encompasses two distinct political regimes: a military regime followed by a democratic one.
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.
We also show the impact of the different political regimes on the vote distributions.
Inspired in multi-species population dynamics, we propose a model,
consisting in a system of nonlinear differential equations with stochastic parameters,
that allows to predict and interpret the observed features.
We show that the distribution of votes among candidates reveals
patterns that reflect the evolution of people interactions.
In particular, a statistical
property of vote distributions, that appears to be predominantly associated
to the electorate, can be used as a measure of its degree of feed-back.
Such measure of a population, which is hard to be accessed otherwise,
may be useful to know the extent to which people interact and can be influenced,
even beyond the context of political elections.