  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.
