Characterizations of egalitarian binary relations as transitive closures with a special reference to Lorenz dominance and to single-crossing conditions

This article considers, in the context of the fixed-population constant-sum comparison of income distributions, a number of intransitive binary relations smaller than Lorenz dominance. We determine their transitive closure, and we study how they relate to each other and to other relations that have appeared in the literature. Among other results, we provide alternative characterizations of Lorenz dominance.