Resource Egalitarianism with a Dash of Efficiency

We study the problem of defining inequality-averse social orderings over the space of allocations in a multi-commodity environment where individuals differ only in their preferences. We formulate notions of egalitarianism based on the axiom that any dominance between the consumption bundles of two individuals should be reduced. This Dominance Aversion requirement is compatible with Consensus, a weak version of the Pareto principle saying that an allocation y is better than x whenever everybody finds that everyone's bundle at y is better than at x. We identify two families of multidimensional leximin orderings satisfying Dominance Aversion and Consensus. We also discuss weaker forms of egalitarianism based on a new definition of multidimensional Lorenz dominance.