# Generalized binary utility functions and fair allocations

arXiv: https://arxiv.org/abs/2109.08461 · HTML: https://mlsanity.com/paper/2109.08461/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2021.

## Built on by (most cited first, 3 of 3)

- [Temporal Fair Division of Indivisible Items](https://mlsanity.com/paper/2410.14593/) (2024)
- [Understanding EFX Allocations: Counting and Variants](https://mlsanity.com/paper/2504.03951/) (2025)
- [The Coordination Gap: Multi-Agent Alternation Metrics for Temporal Fairness in Repeated Games](https://mlsanity.com/paper/2603.05789/) (2026)

## Abstract (arXiv)

The problem of finding envy-free allocations of indivisible goods can not always be solved; therefore, it is common to study some relaxations such as envy-free up to one good (EF1). Another property of interest for efficiency of an allocation is the Pareto Optimality (PO). Under additive utility functions, it is possible to find allocations EF1 and PO using Nash social welfare. However, to find an allocation that maximizes the Nash social welfare is a computationally hard problem. In this work we propose a polynomial time algorithm which maximizes the utilitarian social welfare and at the same time produces an allocation which is EF1 and PO in a special case of additive utility functions called buyer utility functions. Moreover, a slight modification of our algorithm produces an allocation which is envy-free up to any positively valued good (EFX).