PACS 89.65.-s -Social and economic systems PACS 89.75.Da -Systems obeying scaling laws PACS 89.75.-k -Complex systemsAbstract. -Nowadays there is an increasing interest of physicists in finding regularities related to social phenomena. This interest is clearly motivated by applications that a statistical mechanical description of the human behavior may have in our society. By using this framework, we address this work to cover an open question related to elections: the choice of elections candidates (candidature process). Our analysis reveals that, apart from the social motivations, this system displays features of traditional out-of-equilibrium physical phenomena such as scale-free statistics and universality. Basically, we found a non-linear (power law) mean correspondence between the number of candidates and the size of the electorate (number of voters), and also that this choice has a multiplicative underlying process (lognormal behavior). The universality of our findings is supported by data from 16 elections from 5 countries. In addition, we show that aspects of network scale-free can be connected to this universal behavior.

We report on a statistical analysis of the engagement in the electoral processes of all Brazilian cities by considering the number of party memberships and the number of candidates for mayor and councillor. By investigating the relationships between the number of party members and the population of voters, we have found that the functional forms of these relationships are well described by sublinear power laws (allometric scaling) surrounded by a multiplicative log-normal noise. We have observed that this pattern is quite similar to those we previously reported for the relationships between the number of candidates (mayor and councillor) and population of voters [Europhys. Lett. 96, 48001 (2011)], suggesting that similar universal laws may be ruling the engagement in the electoral processes. We also note that the power-law exponents display a clear hierarchy, where the more influential is the political position the smaller is the value of the exponent. We have also investigated the probability distributions of the number of candidates (mayor and councillor), party memberships, and voters. The results indicate that the most influential positions are characterized by distributions with very short tails, while less influential positions display an intermediate power-law decay before showing an exponential-like cutoff. We discuss the possibility that, in addition to the political power of the position, limitations in the number of available seats can also be connected with this changing of behavior. We further believe that our empirical findings point out to an under-representation effect, where the larger the city is, the larger are the obstacles for more individuals to become directly engaged in the electoral process.

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