Approval-Based Voting with Mixed Goods
Xinhang Lu, Jannik Peters, Haris Aziz, Xiaohui Bei, Warut Suksompong
Abstract
We consider a voting scenario in which the resource to be voted upon may consist of both indivisible and divisible goods. This 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.
BibTeX
@article{Lu_Peters_Aziz_Bei_Suksompong_2023, title={Approval-Based Voting with Mixed Goods}, volume={37}, url={https://ojs.aaai.org/index.php/AAAI/article/view/25717}, DOI={10.1609/aaai.v37i5.25717}, abstractNote={We consider a voting scenario in which the resource to be voted upon may consist of both indivisible and divisible goods. This 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.}, number={5}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Lu, Xinhang and Peters, Jannik and Aziz, Haris and Bei, Xiaohui and Suksompong, Warut}, year={2023}, month={Jun.}, pages={5781-5788} }