Multiwinner Approval Voting: An Apportionment Approach

• In Event: Models of Political Institutions

Abstract

The properties of approval voting (AV) in single-winner elections, as well as its use in professional societies, have been extensively studied. But when used for multiwinner elections, such as to elect a committee or city council, AV is vulnerable to the tyranny of the majority, whereby a 51% majority can win all the seats, leaving the 49% minority disenfranchised.

We propose several multiwinner approval voting systems, using approval ballots, that iteratively reduce the support of voters according to the number of their approved candidates who have already been elected. It begins by electing the AV winner, A, after which voters who voted for A have their votes for other candidates depreciated, as with divisor methods of apportionment--such as those proposed by Jefferson (D'Hondt) and Webster (Sainte-Lague)—in assigning seats to parties in a parliament. At each stage in the process, the most deserving candidate, based on his or her depreciated support from voters who have already had approved candidates elected and undepreciated support from voters who have not, receives the next seat.

We analyze the properties of multiwinner approval voting systems, based on different divisor apportionment methods, and compare them with other multiwinner approval systems that have been proposed.

Authors

• Steven J. Brams, New York University

• D. Marc Kilgour, Wilfrid Laurier University

• Richard F. Potthoff