On Multi-Level Apportionment
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866918200336187392 |
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| author | Schmidt-Kraepelin, Ulrike Suksompong, Warut Wijaya, Steven |
| author_facet | Schmidt-Kraepelin, Ulrike Suksompong, Warut Wijaya, Steven |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Multi-Level Apportionment Schmidt-Kraepelin, Ulrike Suksompong, Warut Wijaya, Steven Theoretical Economics Computer Science and Game Theory 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. |
| title | On Multi-Level Apportionment |
| topic | Theoretical Economics Computer Science and Game Theory |
| url | https://arxiv.org/abs/2511.10000 |