Selections from ordered sets
研究如何评估从一个集合中选出的子集与该集合的给定排序之间的接近程度，提出了三个公理并导出一个简单指数，该指数是所选元素秩和的线性函数。
We study the problem of evaluating whether the selection from a set is close to the ordering of the set determined by an exogenously given measure. Our main result is that three axioms, two naturally capturing “dominance”, and a stronger one imposing a form of symmetry in the comparison of selections, are sufficient to evaluate how close any selection from any set is to the given ordering of the set. This closeness is given by a very simple index, which is a linear function of the sum of the ranks of the selected elements. The paper ends by relating this index to the existing literature on distance between orderings, and also offers a practical application of the index.