Fair Division with Binary Valuations: One Rule to Rule Them All

TL;DR

This paper demonstrates that maximum Nash welfare (MNW) provides a fair, efficient, and strategyproof allocation rule for indivisible goods when agents have binary additive preferences, establishing MNW as the definitive solution in this setting.

Contribution

It proves that deterministic MNW with lexicographic tie-breaking is group strategyproof, envy-free up to one good, and Pareto optimal for binary additive preferences, and shows fractional MNW can be implemented as a distribution over such allocations.

Findings

Deterministic MNW is group strategyproof, envy-free up to one good, and Pareto optimal.

Fractional MNW can be realized as a distribution over deterministic MNW allocations.

MNW is established as the ultimate rule for binary additive preferences.

Abstract

We study fair allocation of indivisible goods among agents. Prior research focuses on additive agent preferences, which leads to an impossibility when seeking truthfulness, fairness, and efficiency. We show that when agents have binary additive preferences, a compelling rule -- maximum Nash welfare (MNW) -- provides all three guarantees. Specifically, we show that deterministic MNW with lexicographic tie-breaking is group strategyproof in addition to being envy-free up to one good and Pareto optimal. We also prove that fractional MNW -- known to be group strategyproof, envy-free, and Pareto optimal -- can be implemented as a distribution over deterministic MNW allocations, which are envy-free up to one good. Our work establishes maximum Nash welfare as the ultimate allocation rule in the realm of binary additive preferences.