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.

翻译：我们研究基于个体、团队或对象之间成对比较的排名问题，采用Bradley-Terry模型。该模型中的排名估计通常通过Zermelo近一个世纪前首次提出的简单迭代算法进行。本文描述了一种同样简单但被证明可返回相同结果且速度更快（某些情况下快百倍以上）的替代迭代方法。我们通过一系列示例数据集演示该算法的应用，并推导出关于其收敛性的若干结论。