一类偏好关系的相异度半度量
A class of dissimilarity semimetrics for preference relations
摘要：
我们提出了一类半度量的偏好关系，其中任何一个是一个替代经典的Kemeny-Snell-Bogart度量。(We对于什么构成偏好关系采取一个相当一般的观点，允许任何非循环顺序作为一个。）这些半度量完全基于偏好对选择行为的影响，因此在经济背景和选择实验中显得更合适。在我们的主要结果中，我们得到了一个相当简单的公理化特征的类，我们建议。显然最重要的成员，这一类（至少在有限的情况下替代空间），我们称之为顶差半度量，是其特征分别。我们还获得了它的替代公式，并相对于这个度量，计算完全偏好空间的直径，以及给定的非循环偏好关系的最佳传递扩展。最后，我们证明了我们的偏好度量空间不能等距嵌入在一个欧几里得空间。
英文摘要：
We propose a class of semimetrics for preference relations any one of which is an alternative to the classical Kemeny-Snell-Bogart metric. (We take a fairly general viewpoint about what constitutes a preference relation, allowing for any acyclic order to act as one.) These semimetrics are based solely on the implications of preferences for choice behavior, and thus appear more suitable in economic contexts and choice experiments. In our main result, we obtain a fairly simple axiomatic characterization for the class we propose. The apparently most important member of this class (at least in the case of finite alternative spaces), which we dub the top-difference semimetric, is characterized separately. We also obtain alternative formulae for it, and relative to this metric, compute the diameter of the space of complete preferences, as well as the best transitive extension of a given acyclic preference relation. Finally, we prove that our preference metric spaces cannot be isometically embedded in a Euclidean space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
