Efficient Computation of Rankings from Pairwise Comparisons

M. E. J. Newman.

Year: 2023, Volume: 24, Issue: 238, Pages: 1−25


We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced by Zermelo almost a century ago. Here we describe an alternative and similarly simple iteration that provably returns identical results but does so much faster—over a hundred times faster in some cases. We demonstrate this algorithm with applications to a range of example data sets and derive a number of results regarding its convergence.