This paper is concerned with the problem of ranking and quantifying the extent of deprivation in multidimensional distributions of dichotomous deprivation variables. To this end, we introduce a family of measures of deprivation justified on the basis of dual social evaluation functions. Two alternative criteria of second-degree deprivation count distribution dominance are shown to divide the proposed family of deprivation measures into two separate subfamilies, which can be justified by a combination of correlation increasing and count neutral rearrangements. Based on EU-SILC data, we show that application of the proposed measures might lead to conclusions that differ from those attained by standard cut-off measures, and that results based on cut-off measures are more sensitive to the choice of specific measure.
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