Electorate involvement disorder: Universal relationship between the amplitude and electorate size in second round of Brazilian Presidential Election

Abstract

The voter’s opinion is not expressed exclusively in the vote for one of the candidates, it may be implicit among abstentions or invalid votes, which are blank and null votes. In this study, we investigated the electorate participation in second rounds of Brazilian presidential elections, by consider the list, per ballot box, of the proportions of the three possible “forms of voter participation” in the election result: abstaining from voting, voting blank or null, or voting for one of the candidates, which called here of the electorate involvement. We used the entropy concept of Statistical Mechanics relating these proportions as a measure of the “disorder” of the electoral involvement. We found a generalized logarithmic model, parameter free, for the entropy amplitude per city as a function of the electorate size, showing that the range of the electorate involvement disorder is maintained over all election years and tends to grow more slowly in the larger electorates.