Efficient Algorithms for Paired Comparison Models

Pairwise comparison models are a fundamental tool to infer rankings and preferences from binary outcomes. Starting from the Thurstone-Mosteller and Bradley-Terry formulations, numerous extensions have been proposed to account for ties, covariates, order effects, and time-varying strengths, with applications in psychology, sports, and artificial intelligence. This thesis focuses on the study and computational implementation of such models, emphasizing efficient algorithms for estimating competitor worths and deriving rankings. The first chapter introduces the theoretical foundations and main extensions, with practical examples through the BradleyTerry2 package in R. The second chapter investigates computational aspects, comparing Zermelo’s method, Newman’s algorithm, and MAP (maximum a posteriori) approaches with priors on worth parameters, including experiments on simulated data. The third chapter explores our alternative prior distribution and applies the method to real-world datasets. The goal is to evaluate how different regularizations affect accuracy. Overall, the thesis seeks to combine theoretical developments with algorithmic innovation, providing statistically sound and computationally efficient tools for ranking problems across diverse domains.