This paper proposes a concept of inequality comparisons with ordinal multidimensional 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 correlation-increasing switches and/or median-preserving spreads. For the 2x2 case (with two binary indicators), we derive an operational procedure for checking ordinal inequality relations in practice. As an illustration, we apply the model to childhood poverty in Mozambique.
Sonne-Schmidt, C.; Tarp, F.; Osterdal, L.P. Ordinal multidimensional inequality. UNU-WIDER, Helsinki, Finland (2013) 32 pp. ISBN 978-92-9230-674-8 [WIDER Working Paper No. 2013/097]