PageRank and the Bradley-Terry model
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.
Cite
@article{arxiv.2402.07811,
title = {PageRank and the Bradley-Terry model},
author = {David Antony Selby},
journal= {arXiv preprint arXiv:2402.07811},
year = {2024}
}