Phragmen's voting methods and justified representation

• 成果类型: Article
• 署名作者: Brill, Markus; Freeman, Rupert; Janson, Svante; Lackner, Martin
• 署名单位: Technical University of Berlin; University of Warwick; University of Virginia; Uppsala University; Technische Universitat Wien
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-01926-8
• 发表日期: 2024
• 页码: 47-76
• 关键词: Complexity

摘要

In the late 19th century, Swedish mathematician Edvard Phragmen proposed a load-balancing approach for selecting committees based on approval ballots. We consider three committee voting rules resulting from this approach: two optimization variants-one minimizing the maximum load and one minimizing the variance of loads-and a sequential variant. We study Phragmen 's methods from an axiomatic point of view, focusing on properties capturing proportional representation. We show that the sequential variant satisfies proportional justified representation, which is a rare property for committee monotonic methods. Moreover, we show that the optimization variants satisfy perfect representation. We also analyze the computational complexity of Phragmen 's methods and provide mixed-integer programming based algorithms for computing them.