Distance on matchings: An axiomatic approach
构建了一个规范框架，将个体偏好内生化，量化匹配市场机制结果之间的差异，并找到唯一满足一组自然条件的距离函数类：缩放博尔达距离。
Matchings in a market may have varying degrees of compromise from efficiency, fairness, and or stability. A distance function allows to quantify such concepts or the (dis)similarity between any two matchings. There are a few attempts to propose such functions; however, these are tailored for specific applications and ignore the individual preferences completely. In this paper, we construct a normative framework to quantify the difference between outcomes of market mechanisms in matching markets, while endogenizing the preferences of the individuals into the distance concept. Several conditions are introduced to capture natural and appealing behavior of such functions. We find a class of distance functions called scaled Borda distances , which is the only class of distance functions that satisfies these conditions simultaneously.