Abstract

A coordinated ranking as an opinion of an expert group can be represented by the well-known Kemeny’s median. Such a decision is a least different from other rankings, and is free of some contradictions of the majority rule problem. As a mathematical principle, the Kemeny’s median gives a decision in any case, in particular, for conflicting experts or groups. In practice, competing opinions are usually identified, and special procedures are used to achieve the required level of consensus. One known approach consists in assigning weights to expert opinions. In this paper, the correct mathematical basis is formulated for new types on the Kemeny’s median, like metric and weighted ones. The problem to find the median for a linear combination of expert rankings is investigated based on the well-known locally optimal Kemeny’s algorithm. It is proposed to investigate the rank aggregation problem based on new types of the median.

中文翻译：

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基于新型 Kemeny 中位数的秩聚合

摘要

作为专家组意见的协调排名可以用著名的 Kemeny 中位数表示。这样的决定与其他排名的区别最小，并且没有多数规则问题的一些矛盾。作为数学原理，Kemeny 的中位数在任何情况下都能做出决定，特别是对于相互冲突的专家或团体。在实践中，通常会识别出相互竞争的意见，并使用特殊程序来达到所需的共识水平。一种已知的方法包括为专家意见分配权重。在本文中，为 Kemeny 中位数的新类型制定了正确的数学基础，如公制和加权中位数。基于众所周知的局部最优 Kemeny 算法，研究了寻找专家排名线性组合的中位数的问题。