The many routes to the ubiquitous Bradley-Terry model

2023/12/21 by Ian Hamilton, Nick Tawn, Hamilton, Ian +3 · 2 voices · 1 citation
Economics, Econometrics and Finance · Decision Sciences · #Sports Analytics and Performance #Multi-Criteria Decision Making

paper · pdf · doi:10.48550/arxiv.2312.13619

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.

Cited by

• Convergence analysis of a family of Zermelo-type iterations for the Bradley--Terry model

Discussions

• Hamilton, Tawn, Firth (2023) "The many routes to the ubiquitous Bradley-Terry model": arxiv.org/abs/2312.13619 Very cool! I've considered writing notes on how BT models can be motivated in myriad ways [bsky, 26 points, 0 comments]
• From my end I think I have naively extrapolated the Poisson process argument from Section 6.1 of arxiv.org/abs/2312.13619 where they consider the probability of first occurrence in proper Poisson proc [bsky, 1 points, 1 comments]

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