Comparing degrees of inequality aversion

We propose a straightforward dominance procedure for comparing social welfare orderings (SWOs) with respect to the degree of inequality aversion they express. Three versions of the procedure are considered, each of which uses a different underlying criterion of inequality comparisons: (i) a concept based on the Lorenz quasi-ordering, which we argue to be the ideal version, (ii) a concept based on a minimalist criterion of inequality, and (iii) a concept based on the relative differentials quasi-ordering. It turns out that the traditional Arrow-Pratt approach is equivalent to the latter two concepts for important classes of SWOs, but that it is profoundly inconsistent with the Lorenz-based concept. With respect to the problem of combining extreme inequality aversion and monotonicity, concepts (ii) and (iii) identify as extremely inequality averse a class of SWOs that includes leximin as a special case, whereas the Lorenz-based concept (i) concludes that extreme inequality aversion and monotonicity are incompatible.