Partial Ordering of Unpredictable Mobility with Welfare Implications

Abstract

We propose a partial ordering of ‘unpredictable mobility’ in the spirit of Blackwell's ordering of information structures. The proposed ordering ranks mobility matrices according to the degree to which elements in a given set are likely to move from one state to another, independently of their origin. Furthermore, for an important class of transition structures, our proposed ordering implies ordering, thus carrying significant welfare implications. Moreover, whenever it exists, our partial ordering functions as a sufficient condition for a class of renowned mobility measures and thereby generates, for a subset of transition matrices, unanimous ranking among mobility indices that are not generally consistent with one another.