The Excess Method: A Multiwinner Approval Voting Procedure to Allocate Wasted Votes

In using approval voting to elect multiple winners to a committee or council, it is desirable that excess votes — approvals beyond those that a candidate needs to win a seat — not be wasted. The excess method does this by sequentially allocating excess votes to a voter’s as-yet-unelected approved candidates, based on the Jefferson method of apportionment. It is monotonic — approving of a candidate never hurts and may help him or her get elected — computationally easy, and less manipulable than related methods. In parliamentary systems with party lists, the excess method is equivalent to the Jefferson method and thus ensures the approximate proportional representation of political parties. As a method for achieving proportional representation (PR) on a committee or council, we compare it to other PR methods proposed by Hare, Andrae, and Droop for preferential voting systems, and by Phragmén for approval voting. Because voters can vote for multiple candidates or parties, the excess method is likely to abet coalitions that cross ideological and party lines and to foster greater consensus in voting bodies.