Counting poverty orderings and deprivation curves

Most of the data available for measuring capabilities or dimensions of poverty is either ordinal or categorical. However, the majority of the indices introduced for the assessment of multidimensional poverty behave well only with cardinal variables. The counting approach introduced by Atkinson (2003) concentrates on the number of dimensions in which each person is deprived, and is an appropriate procedure that deals well with ordinal and categorical variables. A method to identify the poor and a number of poverty indices has been proposed taking this framework into account. However, the implementation of this methodology involves the choice of a minimum number of deprivations required in order to be identified as poor. This cut-off adds arbitrariness to poverty comparisons. The aim of this paper is two-fold. Firstly, we explore properties which allow us to characterize the identification method as the most appropriate procedure to identify the poor in a multidimensional setting. Then the paper examines dominance conditions in order to guarantee unanimous poverty rankings in a counting framework. Our conditions are based on simple graphical devices that provide a tool for checking the robustness of poverty rankings to changes in the identification cut-off, and also for checking unanimous orderings in a wide set of multidimensional poverty indices that suit ordinal and categorical data.