Constrained welfare egalitarianism in surplus-sharing problems

We introduce the constrained egalitarian surplus-sharing rule fCE, which distributes an amount of a divisible resource so that the poorer agents’ resulting payoffs become equal but not larger than any remaining agent’s status quo payoff. We show that fCE is characterized by Pareto optimality, nonnegativity, path independence, and less first, a new property requiring that an agent does not gain if her status quo payoff exceeds that of another agent by the surplus. We provide two additional characterizations weakening less first and employing consistency, a classical invariance property with respect to changes of population. We investigate the effects of egalitarian principles in the setting of transferable utility (TU) games. A single-valued solution for TU games is said to support constrained welfare egalitarianism if it distributes any increment of the worth of the grand coalition according to fCE. We show that the set of Pareto optimal single-valued solutions that support fCE is characterized by means of aggregate monotonicity and bounded pairwise fairness, resembling less first.