Mallows 模型廣泛應用於排名聚合問題。該模型由一個中心排名與一個離散參數組成。模型的參數估計通常仰賴於假設觀察到的排名資料在給定模型參數後彼此獨立。然而關於此條件相依性的檢測仍較少被研究。傳統的相關性衡量方法並不適用於此問題，因為來自同一 Mallows 模型的排名配對會因為共同接近中心排名而呈現相關性，例如 Kendall 相關係數與 Spearman 相關係數。本研究提出一個條件置換檢定，用以檢測兩個排名是否存在條件過度相關。本研究亦透過模擬研究與實際資料分析說明所提出方法的有效性。

The Mallows model is widely used for rank aggregation. It is characterized by a central ranking and a dispersion parameter. The estimation of the model parameters often relies on the assumption that the observed ranking lists are mutually independent conditional on the model parameters. However, the detection of the conditional dependence is less studied. Traditional correlation measures such as the Kendall and Spearman correlation do not work here as each ranking pair from the Mallows model is correlated due to their similarity with the central ranking. In this paper, we propose a conditional permutation test to detect whether two rankings are conditionally overly correlated. Simulation studies and real data analyses are provided to illustrate the usefulness of the proposed method.

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