Robust Pro-Poorest Poverty Reduction with Counting Measures : The Anonymous Case

When measuring poverty with counting measures, it is worth inquiring into the conditions prompting poverty reduction which not only reduce the average poverty score further but also decrease deprivation inequality among the poor, thereby emphasizing improvements among the poorest of the poor. For comparisons of cross-sectional datasets of the same society in different periods of time (i.e. an anonymous assessment), the literature offers a second-order dominance condition based on reverse generalized Lorenz curves, whose fulfillment ensures that multidimensional poverty decreases along with a reduction in deprivation inequality for a broad family of inequality-sensitive counting poverty measures. However, the condition holds for a predetermined vector of weights for the poverty dimensions. In this paper we refine this second-order condition in order to obtain necessary and sufficient conditions whose fulfillment ensures that multidimensional poverty reduction is robust to a broad array of weighting vectors and inequality-sensitive poverty measures. We illustrate these methods with an application to multidimensional poverty in Peru