Abstract
Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software.
Highlights
In Brazil, elections for president, governors and mayors use the majority system, where the candidate with absolute majority of the votes is elected
Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique and calculations and simulations were carried out PLOS ONE | DOI:10.1371/journal.pone
Estimates of the percentage of votes of each party/coalition do not allow to forecast the number of seats each party/coalition will receive
Summary
In Brazil, elections for president, governors and mayors use the majority system, where the candidate with absolute majority of the votes is elected. On a proportional system the absolute majority of the votes do not guarantee the election of this candidate. Brazil defines the electoral quotient as the number of valid votes divided by the number of seats. The remaining seats are allocated using the D’Hondt method. These peculiarities of proportional elections make classic statistical inference not viable. The same inference can be carried out using Bayesian inference combined with Monte Carlo simulation methods. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique and calculations and simulations were carried out PLOS ONE | DOI:10.1371/journal.pone.0116924 March 18, 2015
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