Constrained welfare egalitarianism in surplus-sharing problems

The constrained equal welfare rule, fCE, distributes the surplus according to the uniform gains method and, hence, equalizes the welfare of the agents subsequent to the allocation process, subject to making nobody worse off. We show that fCE is the unique rule on the domain of surplus-sharing problems that satisfies efficiency, welfare monotonicity, path independence, and weak less first imposing an egalitarian bound for allowing positive payoffs to particular players. We provide an additional axiomatization employing consistency, a classical invariance property with respect to changes of the population. Finally, we show that the set of efficient solutions for cooperative TU games that support constrained welfare egalitarianism, i.e., distribute increments in the worth of the grand coalition according to fCE, is characterized by aggregate monotonicity and bounded pairwise fairness requiring that a player can only gain if his initial payoff does not exceed the initial payoff of any other player by the amount to be divided.