Introdução a métodos matemáticos de ranking e rating

Abstract

This dissertation aims to introduce some mathematical aspects used to construct ratings and rankings. Ranking consists of ordering items according to certain principles. This process can be found in many contexts, such as socioeconomic index, sports competitions, educational rankings, etc. This work considers the mathematical foundations present in the Gini Index and in the Human Development Index (HDI), and explores, through linear regressions, the correlation between these indicators and the Brazilian results for the Program for International Student Assessment (PISA). Furthermore, the Massey and Elo ranking methods, often used in sports, were characterized. This required a more in-depth study of certain topics in linear algebra and functions, such as: overdetermined linear systems resolution using normal equations, reparameterization and pseudoinverse, and the logistic function. As an educational product, a series of videos was produced on some of the topics considered, in line with the BNCC guidelines.