Compute Phragmén's voting rule online
In the
1890s, Swedish mathematician Lars
Edvard Phragmén proposed a collection of voting rules that would later become known as Phragmén's voting methods. These
rules were initially introduced to address the needs of Swedish elections, which sought a more
representative and proportional process for selecting parliament members, and to decide on party lists.
Phragmén's voting rules are voting methods for multi-winner elections, where the aim is to elect a committee that represents the voters. They are tailored to ensure a proportional outcome, where every voter has approximately equal influence on the outcome.
There are several variants of Phragmén's voting rules. The three main variants include Phragmén's sequential rule, minimax Phragmén, and the Phragmén-Eneström rule. These all work with approval ballots, also called unordered ballots, where voters can vote for an arbitrary number of candidates, without ordering them in order of preferences. However, there are also variants of Phragmén's rules that use ordered ballots.
Click to go to the online ABC voting rule calculator with support for
Phragmén's
voting rules.
This website features a free and easy-to-use online calculator that that allows users to compute the results of Phragmén's various voting methods. By inputting election data, users can observe the outcomes generated by each rule and compare them. The computations are performed on the user's device.
Besides Phragmén's voting methods, the calculator supports many other approval-based committee voting rules, including standard approval voting, Proportional Approval Voting, and the Method of Equal Shares. A total of 27 voting rules are available for immediate computation. The calculator is based on the popular open-source abcvoting python package.
For more information about Phragmén's voting rules, you can refer to the 2023 book Multi-Winner
Voting with Approval Preferences by Martin Lackner and Piotr Skowron, which is published by
Springer and which is available for free for PDF download from the publisher.
You can also refer to the 2016 survey paper "Phragmén's and
Thiele's election methods" by Svante Janson, which discusses historical background, all the
various variants of Phragmén's rules, and their properties.