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.

翻译：PageRank算法与Bradley-Terry模型是两种相互竞争的实体排序方法，适用于体育赛事队伍排名或引文网络中的期刊排序。Bradley-Terry模型是一种基于成对比较的经典统计排序方法，而PageRank算法则根据节点在网络中的重要性进行排序。前者通过最大似然估计计算得分，后者则通过马尔可夫链的平稳分布推导排序。近年来的研究发现，Bradley-Terry模型的最大似然估计值可从这种极限分布近似得出——这一有趣的联系在数十年间被反复发现与重新发现。本文通过相对简洁的数学推导，揭示了利用Bradley-Terry模型的准对称性（quasi-symmetry）所建立的双向关联，从而将成对比较方法与PageRank算法联系在一起。这为Bradley-Terry得分与"缩放版PageRank"之间提供了新颖的互释视角，并对基于引文的期刊排名指标具有直接启示意义。