Phragmén’s voting methods and justified representation

Abstract In the late 19th century, Swedish mathematician Edvard Phragmén 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 maximum load and one variance of loads—and sequential variant. study ’s methods an axiomatic point view, focusing properties capturing proportional representation. show that variant satisfies justified representation , which is rare property monotonic methods. Moreover, we variants satisfy perfect . also analyze computational complexity provide mixed-integer programming algorithms computing them.