We introduce a simple and natural iterative version of the well-known and widely studied Markov rating method. We show that this iterative Markov method converges to the usual global Markov rating, and shares a close relationship with the well-known Elo rating. Together with recent results on the relationship between the global Markov method and the maximum likelihood estimate of the rating vector in the Bradley–Terry (BT) model, we connect and explore the global and iterative Markov, Elo, and Bradley–Terry ratings on real and simulated data.

中文翻译：

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迭代马尔可夫评级法

我们介绍了一个著名的，经过广泛研究的马尔可夫评级方法的简单自然的迭代版本。我们证明了这种迭代马尔可夫方法收敛于通常的全局马尔可夫等级，并且与众所周知的Elo等级有着密切的关系。连同最近在Bradley-Terry（BT）模型中全局Markov方法和评级向量的最大似然估计之间的关系的结果，我们连接并探索了真实的全局和迭代Markov，Elo和Bradley-Terry评级和模拟数据。