The Many Routes to the Ubiquitous Bradley–Terry Model

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 maximizing an objective function; others are derived from well-known statistical models, or stylized game scenarios. They include both examples well-known in the literature as well as what are believed to be novel presentations.