What's So Speciall About Euclidean Distance? A Characterization Result with Applications to Mobility and Spatial Voting

Abstract

In this paper we investigate the problem of measuring social mobility when the social status of individuals is given by their rank. In order to sensibly rep- resent the rank mobility of subgroups within a given society, we address the problem in terms of partial permutation matrices which include standard (“global”) matrices as a special case. We first provide a characterization of a partial ordering on partial matrices which, in the standard case of global matrices, coincides with the well-known “concordance” ordering. We then provide a characterization of an index of rank mo- bility based on partial matrices and show that, in the standard case of comparing two global matrices, it is equivalent to Spearman’s ρ index.