# Fair Division with Binary Valuations: Characterizations

arXiv: https://arxiv.org/abs/2607.10064 · HTML: https://mlsanity.com/paper/2607.10064/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2026.

## Built on by (most cited first, 1 of 1)

- [Fair Division with Strictly Increasing Valuations: A Tight Threshold for Two-Agent EF1 and PO](https://mlsanity.com/paper/2607.23367/) (2026)

## Abstract (arXiv)

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.