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

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 MNWknown 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.

Computing Welfare-Maximizing Fair Allocations of Indivisible Goods

“…The runtime is polynomial in V . Note that, in the important special case in which the valuations are binary, i.e., u i (o) ∈ {0, 1} for all i ∈ N, o ∈ O (Aleksandrov et al 2015;Bouveret and Lemaître 2016;Barman et al 2017;Halpern et al 2020;Darmann and Schauer 2015;Barman, Krishnamurthy, and Vaish 2018), we have V ≤ m, so the run-time is in O(poly(m)).…”