Approval-based apportionment

Markus Brill, Paul Gölz, Dominik Peters (), Ulrike Schmidt-Kraepelin and Kai Wilker
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Markus Brill: TUB - Technical University of Berlin / Technische Universität Berlin
Paul Gölz: CMU - Carnegie Mellon University [Pittsburgh]
Dominik Peters: LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Ulrike Schmidt-Kraepelin: TUB - Technical University of Berlin / Technische Universität Berlin
Kai Wilker: TUB - Technical University of Berlin / Technische Universität Berlin

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Abstract: In the apportionment problem, a fixed number of seats must be distributed among parties in proportion to the number of voters supporting each party. We study a generalization of this setting, in which voters can support multiple parties by casting approval ballots. This approval-based apportionment setting generalizes traditional apportionment and is a natural restriction of approval-based multiwinner elections, where approval ballots range over individual candidates instead of parties. Using techniques from both apportionment and multiwinner elections, we identify rules that generalize the D'Hondt apportionment method and that satisfy strong axioms which are generalizations of properties commonly studied in the apportionment literature. In fact, the rules we discuss provide representation guarantees that are currently out of reach in the general setting of multiwinner elections: First, we show that core-stable committees are guaranteed to exist and can be found in polynomial time. Second, we demonstrate that extended justified representation is compatible with committee monotonicity (also known as house monotonicity).

Date: 2022-07-26
New Economics Papers: this item is included in nep-des
Note: View the original document on HAL open archive server: https://hal.science/hal-03816043v1
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Published in Mathematical Programming, 2022, 203, pp.77--105. ⟨10.1007/s10107-022-01852-1⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03816043

DOI: 10.1007/s10107-022-01852-1

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