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arXiv · 2511.10000

On Multi-Level Apportionment

Ulrike Schmidt-Kraepelin·Warut Suksompong·Steven Wijaya
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Abstract

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.

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BibTeXRIS

Ulrike Schmidt-Kraepelin, Warut Suksompong, Steven Wijaya. 2025-11-13. On Multi-Level Apportionment. https://doi.org/10.1007/s11238-025-10106-3

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