The paper introduces in social choice theory a directional distance function (DDF) that quantifies the level of inefficiency of a given allocation with respect to the utility possibilities frontier. The paper shows that the DDF has a simple geometric interpretation and involves a complete transitive preference relation. If the uility possibilities set is not convex, it is shown that the Rawls welfare function is dual (in a certain sense) to the DDF. Finally a more general class of distance functions is introduced that is shown to be closely related to a large class of welfare functions widely used in the study of economic inequality.

中文翻译：

---

方向距离函数和社会福利：一些公理和对偶性质

该论文在社会选择理论中引入了一个方向距离函数(DDF)，它量化了给定分配相对于效用可能性边界的低效率水平。论文表明，DDF 具有简单的几何解释，并涉及完整的传递偏好关系。如果效用可能性集不是凸的，则表明罗尔斯福利函数与 DDF 是对偶的（在某种意义上）。最后介绍了一类更一般的距离函数，该类距离函数与广泛用于经济不平等研究的一大类福利函数密切相关。