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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2211.12647 |
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| _version_ | 1866913540984537088 |
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| author | Lu, Xinhang Peters, Jannik Aziz, Haris Bei, Xiaohui Suksompong, Warut |
| author_facet | Lu, Xinhang Peters, Jannik Aziz, Haris Bei, Xiaohui Suksompong, Warut |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_12647 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Approval-Based Voting with Mixed Goods Lu, Xinhang Peters, Jannik Aziz, Haris Bei, Xiaohui Suksompong, Warut Computer Science and Game Theory 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. |
| title | Approval-Based Voting with Mixed Goods |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2211.12647 |