{"ID":2842090,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.10000","arxiv_id":"2511.10000","title":"On Multi-Level Apportionment","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.","short_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 sh...","url_abs":"https://arxiv.org/abs/2511.10000","url_pdf":"https://arxiv.org/pdf/2511.10000v1","authors":"[\"Ulrike Schmidt-Kraepelin\",\"Warut Suksompong\",\"Steven Wijaya\"]","published":"2025-11-13T06:10:49Z","proceeding":"econ.TH","tasks":"[\"econ.TH\",\"cs.GT\"]","methods":"[]","has_code":false}