Abstract

The Kemeny median is the well-known method to get a coordinated decision for a group opinion. This ranking is known as the least different from experts’ individual orderings of alternatives. If rankings are immersed in a metric space like points, the median should be the mean ranking from the mathematical point of view. As a result, the correct median should be the center of the set of rankings as points in a metric space. Based on this idea, new types of the median are denoted as the Kemeny metric median and the Kemeny weighted median as another type of the metric one. A new procedure is developed for the linear combination of experts’ rankings to build the weighted median. As it is showed, the locally optimal algorithm can be used as the basis to build all types of Kemeny medians.

中文翻译：

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Kemeny 中位数的发展：新类型和算法

摘要

Kemeny 中位数是一种众所周知的方法，可以为集体意见做出协调决策。该排名被认为与专家对备选方案的个人排序差异最小。如果排名像点一样沉浸在度量空间中，那么从数学的角度来看，中位数应该是平均排名。因此，正确的中位数应该是作为度量空间中的点的一组排名的中心。基于这个想法，新类型的中位数被表示为 Kemeny 度量中位数，而 Kemeny 加权中位数表示为另一种类型的度量。为专家排名的线性组合开发了一种新程序，以构建加权中位数。如图所示，局部最优算法可以作为构建所有类型 Kemeny 中位数的基础。