The method of Eneström and Phragmén for electing a body of representatives by means of open lists

Abstract

The election of a body of representatives through open list voting requires a suitable algorithm to determine which candidates are selected. The option of selecting the most voted candidates has the serious drawback of potentially leaving many voters without representation. In this paper, we study an alternative, fairer algorithm that was proposed at the turn of the 19th century by Gustaf Eneström and Edvard Phragmén. In common with other proposals by Phragmén himself, it is assumed that the voters express themselves by means of approval voting, that is, each voter indicates an unordered list of the candidates that he deems suitable to represent him. Unlike other methods of the same type, here one starts by setting a quota, that is, the number of votes that give the right to a seat. In fact, Eneström and Phragmén’s method may be seen as an extension of the method of largest remainders to open lists instead of closed lists, or also as an adaptation of the single transferable vote to approval voting instead of preferential voting. The properties of this method are studied and compared with those of other methods of the same type.