Conditions for the most robust multidimensional poverty comparisons using counting measures and ordinal variables

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A natural concern with multivariate poverty measures, as well as with other composite indices, is the robustness of their ordinal comparisons to changes in the indices’ parameter values. Applying multivariate stochastic dominance techniques, this paper derives the distributional conditions under which a multidimensional poverty comparison based on the popular counting measures, and ordinal variables, is fully robust to any values of the indices’ parameters. As the paper shows, the conditions are relevant to most of the multidimensional poverty indices in the literature, including the Alkire–Foster family, upon which the UNDP’s “Multidimensional Poverty Index” (MPI) is based. The conditions are illustrated with an example from the EU-SILC data set.