Simplified model relating blank and null votes to voter turnout from Brazilian state elections results

Abstract

Studies investigating opinion dynamics in elections have mainly focused on votes cast for candidates. However, voter opinions can also be expressed through blank and null votes when none of the candidates represents them. Therefore, our study proposed to model blank and null votes in a scenario of only two candidates using data from nine election years for Brazilian state governors that took place in a second round, making a total of 90 elections. We analyzed the relationship between the turnout and votes for each candidate, as well as blank and null votes, representing the three partitions of the votes in a second-round election. We found the behavior scaling laws for all elections and the three partition votes, totalling 270 fits. Combining this result with the probability conservation of the votes over the voter turnout, we developed a model for the blank and null votes depending on a single parameter. The scaling law behavior of blank and null votes allowed us to observe that voters in the larger populations are more difficult to win over.