# On Multi-Level Apportionment

arXiv: https://arxiv.org/abs/2511.10000 · HTML: https://mlsanity.com/paper/2511.10000/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2025.

## Built on by (most cited first, 1 of 1)

- [Multilevel Fair Allocation under Additive Preferences](https://mlsanity.com/paper/2608.24400/) (2026)

## Abstract (arXiv)

Apportionment refers to the well-studied problem of allocating legislative seats among parties or groups with different entitlements. We present a multi-level generalization of apportionment where the groups form a hierarchical structure, which gives rise to stronger versions of the upper and lower quota notions. We show that running Adams' method level-by-level satisfies upper quota, while running Jefferson's method or the quota method level-by-level guarantees lower quota. Moreover, we prove that both quota notions can always be fulfilled simultaneously.