The many routes to the ubiquitous Bradley-Terry model

TL;DR

This paper explores various motivations and derivations of the Bradley-Terry model for rating items based on pairwise comparisons, highlighting its diverse theoretical foundations and applications.

Contribution

It compiles and explains multiple motivations and derivations for the Bradley-Terry model, including well-known and novel perspectives.

Findings

Multiple derivations of the Bradley-Terry model are presented.

The model's motivations range from principles to game scenarios.

The paper clarifies the theoretical underpinnings of the model.

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.