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Approval-based apportionment
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Brill, Markus, Gölz, Paul, Peters, Dominik, Schmidt-Kraepelin, Ulrike and Wilker, Kai (2024) Approval-based apportionment. Mathematical Programming, 203 . pp. 77-105. doi:10.1007/s10107-022-01852-1 ISSN 0025-5610.
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Official URL: http://dx.doi.org/10.1007/s10107-022-01852-1
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).
Item Type: | Journal Article | ||||||||
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Subjects: | J Political Science > JF Political institutions (General) Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||
Library of Congress Subject Headings (LCSH): | Apportionment -- Mathematical models, Proportional representation, Apportionment (Election law), Representative government and representation, Game theory -- Mathematical models | ||||||||
Journal or Publication Title: | Mathematical Programming | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0025-5610 | ||||||||
Official Date: | January 2024 | ||||||||
Dates: |
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Volume: | 203 | ||||||||
Page Range: | pp. 77-105 | ||||||||
DOI: | 10.1007/s10107-022-01852-1 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 2 November 2022 | ||||||||
Date of first compliant Open Access: | 2 November 2022 | ||||||||
RIOXX Funder/Project Grant: |
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