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.
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