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On Multi-Level Apportionment

Author

Listed:
  • Ulrike Schmidt-Kraepelin
  • Warut Suksompong
  • Steven Wijaya

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.

Suggested Citation

  • Ulrike Schmidt-Kraepelin & Warut Suksompong & Steven Wijaya, 2025. "On Multi-Level Apportionment," Papers 2511.10000, arXiv.org.
    • Handle: RePEc:arx:papers:2511.10000
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    References listed on IDEAS

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    1. Steven J. Brams & D. Marc Kilgour & Richard F. Potthoff, 2019. "Multiwinner approval voting: an apportionment approach," Public Choice, Springer, vol. 178(1), pages 67-93, January.
    2. Yukio Koriyama & Jean-François Laslier & Antonin Macé & Rafael Treibich, 2013. "Optimal Apportionment," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 584-608.
    3. Karpov, Alexander, 2015. "Alliance incentives under the D’Hondt method," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 1-7.
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