# Fair and Efficient Allocations under Lexicographic Preferences

arXiv: https://arxiv.org/abs/2012.07680 · HTML: https://mlsanity.com/paper/2012.07680/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [The Fairness Fair: Bringing Human Perception into Collective Decision-Making](https://mlsanity.com/paper/2312.14402/) (2023)
- [On the existence of EFX allocations in multigraphs](https://mlsanity.com/paper/2502.09777/) (2025)
- [Constrained Serial Dictatorships can be Fair](https://mlsanity.com/paper/2301.06086/) (2023)
- [First-Choice Maximality Meets Ex-ante and Ex-post Fairness](https://mlsanity.com/paper/2305.04589/) (2023)

## Abstract (arXiv)

Envy-freeness up to any good (EFX) provides a strong and intuitive guarantee of fairness in the allocation of indivisible goods. But whether such allocations always exist or whether they can be efficiently computed remains an important open question. We study the existence and computation of EFX in conjunction with various other economic properties under lexicographic preferences--a well-studied preference model in artificial intelligence and economics. In sharp contrast to the known results for additive valuations, we not only prove the existence of EFX and Pareto optimal allocations, but in fact provide an algorithmic characterization of these two properties. We also characterize the mechanisms that are, in addition, strategyproof, non-bossy, and neutral. When the efficiency notion is strengthened to rank-maximality, we obtain non-existence and computational hardness results, and show that tractability can be restored when EFX is relaxed to another well-studied fairness notion called maximin share guarantee (MMS).