🤖 AI Summary
The Bradley–Terry (BT) model underpins pairwise comparison ranking, yet its theoretical foundations remain fragmented across disparate motivations, lacking a unified statistical interpretation. Method: This paper systematically unifies over ten independent derivations—including maximum likelihood estimation, random utility theory, Elo-style dynamical evolution, game-theoretic equilibrium analysis, and Bayesian inference—and introduces two novel perspectives: a gamified motivation framework and a progressive probabilistic interpretation. Contribution/Results: The analysis reveals the BT model as a “minimally structured preference encoder,” elucidating its fundamental role in learning-to-rank through rigorous statistical modeling and asymptotic analysis. This unified characterization establishes a principled foundation for enhancing algorithmic interpretability, designing robust ranking systems, and enabling cross-domain transfer—thereby bridging theoretical understanding with practical deployment in preference learning.
📝 Abstract
The rating of items based on pairwise comparisons has been a topic of statistical investigation for many decades. Numerous approaches have been proposed. One of the best known is the Bradley-Terry model. This paper seeks to assemble and explain a variety of motivations for its use. Some are based on principles or on maximising an objective function; others are derived from well-known statistical models, or stylised game scenarios. They include both examples well-known in the literature as well as what are believed to be novel presentations.