The Excess Method: Avoiding Wasted Votes in Multiwinner Approval Voting

• In Event: Alternative Voting Schemes

Abstract

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. The excess method does this by sequentially allocating excess votes to a voter’s as-yet-unelected approved candidates, based on the Jefferson/d’Hondt apportionment method. It can be seen as a form of subset-manipulation of this method whereby a subset of voters can, by approving of fewer candidates, induce the election of a candidate they approve of who would not otherwise win. The transfer of excess votes satisfies two principles: (i) voter sovereignty—transfers from a winner W go only to unelected candidates that W voters approve of; and (ii) voter equality—the number of excess votes transferred cannot exceed the number of voters to whom it is transferred and so never gives its recipients more than one vote. In parliamentary systems with party lists, the excess method is equivalent to the Jefferson/d’Hondt method and thus ensures the approximate proportional representation of political parties. Because voters can vote for more than one party, it is likely to abet coalitions that cross ideological and party lines, thereby fostering greater consensus in a voting body.

Author

• Steven J. Brams, New York University