Ethically Robust Comparisons of Distributions of Two Individual Attributes

This paper examines the normative properties of an empirically implementable dominance criterion for comparing alternative distributions of two attributes, one of which being cardinally measurable, between an arbitrary number of individuals. The criterion, which generalizes the one proposed by Bourguignon (1989), states that distribution A dominates distribution B when poverty in the cardinally measurable attribute, as measured by the poverty gap, is no greater in A than in B for all poverty lines that are weakly decreasing with respect to the other attribute. The criterion is shown to be equivalent to the ranking of distributions of two attributes that would be aggreed upon by all utility-inequality averse welfarist social planners who assume that households convert attributes into well-being by the same increasing utility function satisfying the property that the marginal utility of the cardinally measurable attribute is decreasing with respect to the two attributes. This paper also identifies the elementary equalizing transformations that correspond to this criterion.