We address the problem of ranking distributions of attributes in terms of poverty, when the attributes are represented by binary variables. To accomplish this task, we identify a suitable notion of "multidimensional poverty line" and characterize axiomatically the Head-Count and the Attribute-Gap poverty rankings, which are the natural counterparts of the most widely used income poverty indices. Finally, we apply our methodology and compare our empirical results with those obtained with some other well-known poverty measures.
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