An extension of Zermelo's model for ranking by paired comparisons
An extension of Zermelo's model for ranking by paired comparisons
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DOI：
10.1017/s0956792500004150
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发表时间：
2000-06-01
影响因子：
1.9
通讯作者：
Grant, CP
中科院分区：
文献类型：
--
作者：
Conner, GR;Grant, CP
Zermelo在1929年提出了一种配对比较排序的概率模型，并证明当结果矩阵不可约时，该模型对所考虑的对象产生唯一的排序。当矩阵可约时，模型可能只产生对象的部分排序。在本文中，我们分析了由奇异扰动引起的Zermelo模型的自然扩展。我们证明了这种扩展产生了任意（非负）结果矩阵的排序，并保留了原始模型的几个理想属性。此外，我们还讨论了计算技术并提供了它们的使用示例。
In 1929, Zermelo proposed a probabilistic model for ranking by paired comparisons and showed that this model produces a unique ranking of the objects under consideration when the outcome matrix is irreducible. When the matrix is reducible, the model may yield only a partial ordering of the objects. In this paper, we analyse a natural extension of Zermelo's model resulting from a singular perturbation. We show that this extension produces a ranking for arbitrary (nonnegative) outcome matrices and retains several of the desirable properties of the original model. In addition, we discuss computational techniques and provide examples of their use.