This paper introduces a concept of inequality comparisons with ordinal
bivariate categorical data. In our model, one population is more
unequal than another when they have common arithmetic median outcomes
and the first can be obtained from the second by correlationincreasing
switches and/or median-preserving spreads. For the canonical
2x2 case (with two binary indicators), we derive a simple operational
procedure for checking ordinal inequality relations in practice.
As an illustration, we apply the model to childhood deprivation in
Mozambique.