  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 form of these
relationships are well described by sub-linear power laws (allometric scaling)
surrounded by a multiplicative log-normal noise. We have observed that this
pattern is quite similar to those previously-reported for the relationships
between the number candidates (mayor and councillor) and population of voters
[EPL 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 councilor), 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 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 underrepresentation effect, where
the larger city is, the larger are the obstacles for more individuals to become
directly engaged in the electoral process.
