When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds

We study the problem of rationing a divisible good among a group of people. Each person's preferences are characterized by an ideal amount that he would prefer to receive and a minimum quantity that he will accept: any amount less than this threshold is just as good as receiving nothing at all. Any amount beyond his ideal quantity has no effect on his welfare. We search for Pareto-efficient, strategy-proof, and envy-free rules. The definitions of these axioms carry through from the more commonly studied problem without disposability or acceptance thresholds. However, these are not compatible in the model that we study. We adapt the equal-division lower bound axiom and propose another fairness axiom called awardee-envy-freeness. Unfortunately, these are also incompatible with strategy-proofness. We characterize all of the Pareto-efficient rules that satisfy these two properties. We also characterize all Pareto-efficient, strategy-proof, and non-bossy rules. (C) 2011 Elsevier Inc. All rights reserved.