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

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## Abstract

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.

## Keywords

Survival Function Poverty Line Poverty Measure Dominance Condition Multidimensional Poverty## Notes

### Acknowledgments

I would like to thank two anonymous referees for very helpful comments, and Gordon Anderson and Casilda Lasso de la Vega for substantial comments on earlier drafts. I would also like to thank Carlos Gradin, Nicole Rippin, Suman Seth, Jose Manuel Roche, Sabina Alkire, Julie Lichtfield, Paul Segal and participants at the 32nd IARIW Conference, University of the Basque Country, Maastricth School of Governance, OPHI, and the XVI IEA World Congress for helpful comments. I would like to thank the European Commission, Eurostat, for permission to use the EU-SILC 2007 user database, release 2 August 2009, under contract EU-SILC/2009/33 between Eurostat and University of Oxford and its Colleges. Eurostat has no responsibility for the results or the conclusions of this paper.

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