On multi-level apportionment

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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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Funding Information
  • National Science Foundation (DMS-1928930)
  • Alfred P. Sloan Foundation (G-2021-16778)
  • Ministry of Education - Singapore (MOE-T2EP20221-0001)
  • National University of Singapore

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