论文标题
偏好关系的一类差异半学分
A class of dissimilarity semimetrics for preference relations
论文作者
论文摘要
我们提出了一类用于偏好关系的半学分，其中任何一种是经典的凯梅尼 - 奈尔 - 纳尔 - 博格特指标的替代方案。 （我们对构成偏好关系的构成的观点相当普遍，允许任何无环的顺序充当一个。）这些半学分仅基于偏好对选择行为的含义，因此在经济环境和选择实验中似乎更合适。在我们的主要结果中，我们为我们提出的类别获得了相当简单的公理表征。该类别中最重要的成员（至少在有限的替代空间的情况下），我们将其配置为最高差异的半明文。我们还获得了它的替代公式，相对于该度量，我们计算了完全偏好的空间的直径，以及给定的无环偏好关系的最佳及时延伸。最后，我们证明我们的偏好度量空间不能等于等立欧几里得空间。
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.
