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Fair Division with Binary Valuations: Characterizations

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  • Florian Brandl
  • Warut Suksompong
  • Nicholas Teh

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.

Suggested Citation

  • Florian Brandl & Warut Suksompong & Nicholas Teh, 2026. "Fair Division with Binary Valuations: Characterizations," Papers 2607.10064, arXiv.org.
    • Handle: RePEc:arx:papers:2607.10064
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    File URL: https://arxiv.org/pdf/2607.10064
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