# Multilevel Fair Allocation under Additive Preferences

arXiv: https://arxiv.org/abs/2608.24400 · HTML: https://mlsanity.com/paper/2608.24400/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 12 of 12)

- [Almost Envy-Freeness in Group Resource Allocation](https://mlsanity.com/paper/1901.08463/) (2019)
- [Weighted Envy-Freeness in Indivisible Item Allocation](https://mlsanity.com/paper/1909.10502/) (2019)
- [Fair Division with Allocator's Preference](https://mlsanity.com/paper/2310.03475/) (2023)
- [Fair Division via Social Comparison](https://mlsanity.com/paper/1611.06589/) (2016)
- [For One and All: Individual and Group Fairness in the Allocation of Indivisible Goods](https://mlsanity.com/paper/2302.06958/) (2023)
- [Group Envy Freeness and Group Pareto Efficiency in Fair Division with Indivisible Items](https://mlsanity.com/paper/2006.15893/) (2020)
- [Weighted Fairness Notions for Indivisible Items Revisited](https://mlsanity.com/paper/2112.04166/) (2021)
- [Envy-Free Allocations Respecting Social Networks](https://mlsanity.com/paper/2011.11596/) (2020)
- [Maximin Fair Allocation of Indivisible Items under Cost Utilities](https://mlsanity.com/paper/2407.13171/) (2024)
- [Putting Fair Division on the Map](https://mlsanity.com/paper/2504.20161/) (2025)
- [On Multi-Level Apportionment](https://mlsanity.com/paper/2511.10000/) (2025)
- [Multilevel Fair Allocation with Matroid-Rank Preferences](https://mlsanity.com/paper/2512.24105/) (2025)

## Abstract (arXiv)

We study multilevel fair resource allocation with tree-structured hierarchical relations among agents. At each level, the problem can be viewed locally as allocating an agent's bundle to its children, the overall allocation being a trace of this process iterated down to the leaves. Assuming that internal nodes' utilities are the utilitarian welfare of their children, and the leaves have classical additive utilities over items, we first propose multilevel adaptations of usual envy-based fairness notions (e.g., WEF1). We present three adaptations and show that the choice among them is not neutral. We prove that, under identical preferences, the three adapted envy-based notions coincide, and that the Multilevel extension of Weighted Round Robin (Chakraborty et al., 2021) (MWRR) guarantees them. We then show that under general preferences, MWRR may guarantee some notions while failing others. Finally, through experiments, we show that MWRR may still perform well even for adaptations it does not formally guarantee.