Inequality ranking of ordered categorical distributions: A status-based approach

One of the basic questions that arise in measuring inequality in the distribution of a variable is how to define the inequality dominance relation (IDR) on the set of alternative distributions i.e. how to decide whether a particular distribution of the variable is to be considered to be no more unequal than another. Important advances in this line of research have been made in the case where the variable in question is cardinally measured. The case of ordinal variables, however, is a relatively unexplored area. This paper considers the case of ordered categorical variables. It adopts an approach to inequality ranking based on the notion of ‘status’ of the individuals and formulates a definition of the IDR by using a new a priori condition, Status Majorization, that one would intuitively expect this relation to satisfy. It is shown that the IDR, so defined, is compatible with the condition of Hammond Majorization. An empirical relation (i.e. a relation defined in terms of observed data) that implements the suggested definition is also obtained. An illustrative application is reported.