The Excess Method: A Multiwinner Approval Voting Procedure to Allocate Wasted Votes
Social Science Research Network
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
... ethods. 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. 4 The main modification of approval voting we analyze, which builds on the Jefferson method, seeks to prevent voters, insofar as possible, from wasting their votes. More specifically, the excess method largely eliminates the need for voters to anticipate the voting behavior of other voters and vote strategically (in particular, so as not to waste votes on shoo-ins, who would win without a voter's support). Instead, it takes the excess approvals that the most popular candidates receive, after they have been elected, and transfers them to a voter's other approved but less popular candidates, who in later rounds deserve, and may benefit from, receiving this additional support. This is not to say that the excess method is invulnerable to manipulation through the misrepresentation of approvals (e.g., Lackner and Skowron, 2018). Sometimes voters can achieve a preferred outcome by withholding approvals from shoo-ins and concentrating their support on the remaining candidates. This form of strategic voting is called subset manipulation, because a voter approves of only a subset of his or her originally approved candidates on the manipulated ballot. Recently, Peters (2018) proved an important impossibility result: If an approvalbased multiwinner voting procedure satisfies a modest degree of PR, it is necessarily susceptible to subset manipulations, dashing hope of finding a rule that is not manipulable-that is, one that is strategyproof. 4 Nevertheless, some rules are less manipulable than others, which is the key insight that motivates the excess method. The excess method not only provides voters with the flexibility of voting for multiple candidates, using an approval ballot, but it also 4 For a broader analysis of the manipulability of voting systems, see Taylor (2005) .