Phragmén's voting methods and justified representation.

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 the maximum load and one minimizing the variance of loads-and a sequential variant. We study Phragmén 's methods from an axiomatic point of view, focusing on properties capturing proportional representation.