Phragmén's voting methods and justified representation

Conference item

In the late 19th century, Lars 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 maximal load and one minimizing the variance of loads—and a sequential variant. We study Phragmen’s methods from an axiomatic point of view, ´ focussing on justified representation and related properties that have recently been introduced by Aziz et al. (2015a) and Sanchez-Fern ´ andez et al. (2017). We show that the sequential ´ variant satisfies proportional justified representation, making it the first known polynomial-time computable method with this property. 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.

Authors: Brill, M; Freeman, R; Janson, S; Lackner, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: AAAI Press
• Host title: Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI'17)
• Journal: AAAI Conference on Artificial Intelligence
• Pages: 406-413
• Publication date: 2017-01-01
• Acceptance date: 2016-11-12
• ISSN: 2159-5399
• Keywords: load balancing; approval ballots; representation; committee voting