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, especially a shoo-in, needs to win a seat—not be wasted. Common voting procedures such as sequential proportional approval voting (seqPAV) elect candidates in sequence and depreciate the voting weights of voters who have gotten one or more of their approved candidates elected. As a consequence, a voter is “punished” for approving a candidate when his or her approval was not necessary for that candidate to be elected. To alleviate this problem, we propose a modification of seqPAV that we call the excess method. In each round, the method determines the excess votes of the winning candidate and transfers them to other candidates approved of by the winner’s supporters. In doing so, the excess method transforms wasted votes into support of a voter’s other approved candidates, who in later rounds deserve, and may benefit from, receiving this additional support. In parliamentary systems with party lists, the excess method is equivalent to seqPAV and thus ensures the approximate proportional representation of political parties. When voters are restricted to voting for a single party list, both methods coincide with the well-known apportionment method due to Jefferson/D’Hondt.