A matemática no processo eleitoral por meio da estatística

Abstract

This study aims to present the role of mathematics in the electoral process through statistics, which are fundamentally important for clarifying doubts held by parts of society. Furthermore, it seeks to demonstrate how statistics are used—through practical examples—in the vote counting process in Brazil, especially in proportional elections. During the development of the research, the following questions arose: How are statistical calculations carried out to determine the results of proportional elections for the City Council, the Chamber of Deputies, and the Legislative Assembly? Why are candidates with fewer votes sometimes elected? In light of these questions, this study is grounded in the general objective of analyzing the importance of mathematics, through statistics, in the vote counting process of proportional elections in Brazil. The specific objectives are: To distinguish between majoritarian and proportional elections; To understand how the seat allocation calculations are performed in Brazil’s proportional elections; To identify the main methods and selection criteria used in elections, particularly proportional ones; To learn how to calculate the "leftover seats" (sobra de vagas) in the electoral process according to the Brazilian Electoral Code (Law No. 4,737/1965); To understand why, in some cases, less-voted candidates are elected. The methodology of this study is characterized as a descriptive research, with both quantitative and qualitative approaches, based on bibliographic sources. This work is relevant both to society—by contributing to a better understanding of how the electoral process functions—and to future researchers in the field, as it successfully achieved its objectives and described the electoral process, particularly the functioning of proportional elections in Brazil