Inequality Measures for Intersecting Lorenz Curves: an Alternative Weak Ordering

The Lorenz ordering is probably the most logical tool for comparison of the dispersion of non negative random variables. Indeed, many income inequality metrics are order preserving (or isotonic) with the aforementioned preorder. However, in some situations Lorenz curves may intersect and the ordering is not fulfilled. Hence, some weaker criteria need to be to introduced: we present a new different preorder, weaker than the Lorenz ordering, and propose a possible class of functionals that preserve it. This method could be especially useful under conditions of maximum uncertainty.