PageRank and the Bradley-Terry model

David Antony Selby

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arXiv · 2402.07811

PageRank and the Bradley-Terry model

David Antony Selby

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Abstract

PageRank and the Bradley-Terry model are competing approaches to ranking entities such as teams in sports tournaments or journals in citation networks. The Bradley-Terry model is a classical statistical method for ranking based on paired comparisons. The PageRank algorithm ranks nodes according to their importance in a network. Whereas Bradley-Terry scores are computed via maximum likelihood estimation, PageRanks are derived from the stationary distribution of a Markov chain. More recent work has shown maximum likelihood estimates for the Bradley-Terry model may be approximated from such a limiting distribution, an interesting connection that has been discovered and rediscovered over the decades. Here we show - through relatively simple mathematics - a connection between paired comparisons and PageRank that exploits the quasi-symmetry property of the Bradley-Terry model. This motivates a novel interpretation of Bradley-Terry scores as 'scaled' PageRanks, and vice versa, with direct implications for citation-based journal ranking metrics.

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David Antony Selby. 2024-02-12. PageRank and the Bradley-Terry model. https://arxiv.org/abs/2402.07811

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