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We report on a statistical analysis of the engagement in the electoralprocesses of all Brazilian cities by considering the number of partymemberships and the number of candidates for mayor and councillor. Byinvestigating the relationships between the number of party members and thepopulation of voters, we have found that the functional form of theserelationships are well described by sub-linear power laws (allometric scaling)surrounded by a multiplicative log-normal noise. We have observed that thispattern is quite similar to those previously-reported for the relationshipsbetween the number candidates (mayor and councillor) and population of voters[EPL 96, 48001 (2011)], suggesting that similar universal laws may be rulingthe engagement in the electoral processes. We also note that the power lawexponents display a clear hierarchy, where the more influential is thepolitical position the smaller is the value of the exponent. We have alsoinvestigated the probability distributions of the number of candidates (mayorand councilor), party memberships and voters. The results indicate that themost influential positions are characterized by distributions with veryshort-tails, while less influential positions display an intermediate power lawdecay before showing an exponential-like cutoff. We discuss that, in additionto the political power of the position, limitations in the number of availableseats can also be connected with this changing of behavior. We further believethat our empirical findings point out to an underrepresentation effect, wherethe larger city is, the larger are the obstacles for more individuals to becomedirectly engaged in the electoral process.

Engagement in the electoral processes: scaling laws and the role of the political positions