Mathematical Models for Ranking from Paired Comparisons
Mathematical Models for Ranking from Paired Comparisons
复制标题
配对比较排名的数学模型
DOI：
10.1080/01621459.1960.10482078
复制
发表时间：
1960
影响因子：
3.7
通讯作者：
H. D. Brunk
中科院分区：
文献类型：
--
作者：
H. D. Brunk
本文简要介绍了两类模型中的几种模型：（1）假设项目的每个可能的排序都有一个“效用”，它取决于配对比较中项目的预期得分。特别是，一个项目的“价值”可以根据与其他项目相比的预期得分来定义。(II)每个项目都被假定有一个内在价值;这些内在价值决定了预期的分数。引入了正则性的概念。在（I）中，讨论了一般的线性效用，并给出了线性效用正则的一个充要条件。在（II）项下，引入了“最小假设”模型。设e（u，v）表示一个价值为u的项目与价值为v的项目相比的期望得分，假设e（u，v）在u中不减，在v中不增。讨论了该模型中期望得分的估计问题。
Abstract Brief mention is made of several models in each of two categories: (I) Each possible ranking of items is assumed to have a “utility” which depends on the expected scores of the items in paired comparisons. In particular, the “worth” of an item may be defined in terms of its expected scores in comparisons with others. (II) Each item is assumed to have an intrinsic worth; these intrinsic worths determine the expected scores. A concept, “regularity” is introduced. Under (I), general linear utilities are discussed, and a necessary and sufficient condition is given in order that a linear utility may be regular. Under (II), a “minimum assumption” model is introduced. Let e(u, v) denote the expected score of an item of worth u when compared with one of worth v. The assumption is: e(u, v) is non-decreasing in u, non-increasing in v. The problem of estimating expected scores in this model is discussed.