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Counting poverty measures have gained prominence in the analysis of multidimensional poverty in recent decades. Poverty orderings based on these measures typically depend on methodological choices regarding individual poverty functions, poverty cut-offs, and dimensional weights whose impact on poverty rankings is often not well understood. In this paper we propose new dominance conditions that allow the analyst to evaluate the robustness of poverty comparisons to those choices. These conditions provide an approach to evaluating the sensitivity of poverty orderings superior to the common approach of considering a restricted and arbitrary set of indices, cut-offs, and weights. The new criteria apply to a broad class of counting poverty measures widely used in empirical analysis of poverty in developed and developing countries including the multidimensional headcount and the adjusted headcount ratios. We illustrate these methods with an application to time-trends in poverty in Australia and cross-regional poverty in Peru. Our results highlight the potentially large sensitivity of poverty orderings based on counting measures and the importance of evaluating the robustness of results when performing poverty comparisons across time and regions.

A recent literature on inequality of opportunity offers quantitative tools for comparisons and measurement based on stochastic dominance criteria and traditional inequality indices. In this paper I suggest an additional way of assessing inequality of opportunity with two indices of dissimilarity across distributions. The indices are based on a traditional homogeneity test of multinomial distributions and are similar to the square coefficient of variation (Reardon and Firebaugh, Sociol Method 32:33–67, 2002). Their properties are studied, as well as their usefulness and limitations in applications when both circumstances and advantages/outcomes are multidimensional. An empirical application measures changes in inequality of opportunity from an old to a young cohort in Peru. The importance of assessing the sensitivity of the results to group definitions and group proportions is highlighted.