# On Maximum Weighted Nash Welfare for Binary Valuations

arXiv: https://arxiv.org/abs/2204.03803 · HTML: https://mlsanity.com/paper/2204.03803/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2022.

## Built on by (most cited first, 6 of 6)

- [Temporal Fair Division of Indivisible Items](https://mlsanity.com/paper/2410.14593/) (2024)
- [Online Fair Division with Additional Information](https://mlsanity.com/paper/2505.24503/) (2025)
- [Not in My Backyard! Temporal Voting Over Public Chores](https://mlsanity.com/paper/2508.08810/) (2025)
- [Yankee Swap: a Fast and Simple Fair Allocation Mechanism for Matroid Rank Valuations](https://mlsanity.com/paper/2206.08495/) (2022)
- [Understanding EFX Allocations: Counting and Variants](https://mlsanity.com/paper/2504.03951/) (2025)
- [Fairness in Repeated Matching: A Maximin Perspective](https://mlsanity.com/paper/2510.04624/) (2025)

## Abstract (arXiv)

We consider the problem of fairly allocating indivisible goods to agents with weights representing their entitlements. A natural rule in this setting is the maximum weighted Nash welfare (MWNW) rule, which selects an allocation maximizing the weighted product of the agents' utilities. We show that when agents have binary valuations, a specific version of MWNW is resource- and population-monotone, satisfies group-strategyproofness, and can be implemented in polynomial time.