The Excess Method: Multiwinner Approval Voting Without Wasted Votes

• In Event: Electoral Systems, Electoral Incentives, and Political Actors

Abstract

A central concern in electing multiple winners to a committee or council is that votes not be wasted. In particular, if a candidate appears to be either a shoo-in or a sure loser, voters would be well advised to vote for other candidates for whom their votes are more likely to make a difference.

We propose an extension of approval voting, called the excess method, to the election of multiple winners. It ensures that approval votes are not wasted--in particular, on shoo-ins. It works in stages, first to depreciate the approval votes of voters who have had one or more candidates already elected, using the Jefferson or Webster apportionment method. Then the excess votes by which a candidate wins a seat are reallocated to other candidates of whom the voter approves, and the apportionment reapplied, until all seats are filled.

We compare the excess method with other methods for handling surplus votes, including that for preferential voting proposed by Hare and Droop and that for approval voting proposed by Phragmén. Although the excess method is not strategy-proof, it largely relieves the voter of the need to assess the candidates' chances of winning a seat in order to cast his or her votes efficiently. It also ensures the approximate proportional representation of political parties--when voting is for parties rather than individuals--and it can be computed efficiently.

Authors

• Steven J. Brams, New York University

• Markus Brill, TU Berlin