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Erscheinungsjahr: 
2024
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[Journal:] Social Choice and Welfare [ISSN:] 1432-217X [Volume:] 62 [Issue:] 4 [Publisher:] Springer Berlin Heidelberg [Place:] Berlin/Heidelberg [Year:] 2024 [Pages:] 643-677
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Springer Berlin Heidelberg, Berlin/Heidelberg
Zusammenfassung: 
Abstract We consider a voting scenario in which the resource to be voted upon may consist of both indivisible and divisible goods. This setting generalizes both the well-studied model of multiwinner voting and the recently introduced model of cake sharing. Under approval votes, we propose two variants of the extended justified representation (EJR) notion from multiwinner voting, a stronger one called EJR for mixed goods (EJR-M) and a weaker one called EJR up to 1 (EJR-1) . We extend three multiwinner voting rules to our setting—GreedyEJR, the method of equal shares (MES), and proportional approval voting (PAV)—and show that while all three generalizations satisfy EJR-1, only the first one provides EJR-M. In addition, we derive tight bounds on the proportionality degree implied by EJR-M and EJR-1, and investigate the proportionality degree of our proposed rules.
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A Correction to this article was published on 28 March 2024: https://doi.org/10.1007/s00355-024-01521-6
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