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Is the preference of the majority representative ?
Mathematical Social Sciences ( IF 0.6 ) Pub Date : 2021-04-20 , DOI: 10.1016/j.mathsocsci.2021.04.001
Mihir Bhattacharya , Nicolas Gravel

We show that a majoritarian relation is, among all conceivable binary relations, the most representative of the profile of preferences from which it emanates. We define “the most representative” to mean that it minimizes the sum of distances between itself and the preferences in the profile for a given distance function. We identify a necessary and sufficient condition for such a distance to always be minimized by a majoritarian relation. This condition requires the distance to be additive with respect to a plausible notion of compromise between preferences. The well-known Kemeny distance does satisfy this property, along with many others. All distances that satisfy this property can be written as a sum of strictly positive weights assigned to the ordered pairs of alternatives by which any two preferences differ.



中文翻译:

是多数代表的偏爱吗?

我们表明,在所有可能的二元关系中,多数派关系是它所产生的偏好概况的最有代表性的代表。我们定义“最具代表性”是指它使自身与给定距离函数的配置文件中的首选项之间的距离之和最小。我们确定了这样的距离的必要和充分条件,该距离总是通过多数派关系最小化。这种条件要求距离相对于偏好之间折衷的合理概念是相加的。众所周知的Kemeny距离以及其他许多特性确实满足了此属性。满足此属性的所有距离都可以写为分配给有选择的成对对的严格正权重的总和,任意两个偏好的差值都不同。

更新日期:2021-04-20
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