Measurement of Inequality with a Finite Number of States: Majorization Concepts for Ordered Response Data

With ordered response data, the numerical scale defining the status of individuals is unknown. In this paper we characterize the set of increasing scales such that some distribution is majorized by another distribution We show that though this set is infinite, it is generated as the convex hull of a finite number of points. Within our framework, we then examine conditions under which it becomes possible to construct partial orderings in practical applications, involving a comparison of a number of distributions