Satisfaction Approval Voting

36 Pages Posted: 16 May 2010

See all articles by Steven J. Brams

Steven J. Brams

New York University (NYU) - Wilf Family Department of Politics

D. Marc Kilgour

Wilfrid Laurier University

Multiple version iconThere are 2 versions of this paper

Date Written: April 14, 2010


We propose a new voting system, satisfaction approval voting (SAV), for multiwinner elections, in which voters can approve of as many candidates or as many parties as they like. However, the winners are not those who receive the most votes, as under approval voting (AV), but those who maximize the sum of the satisfaction scores of all voters, where a voter’s satisfaction score is the fraction of his or her approved candidates who are elected. SAV may give a different outcome from A – in fact, SAV and AV outcomes may be disjoin – but SAV generally chooses candidates representing more diverse interests than does AV (this is demonstrated empirically in the case of a recent election of the Game Theory Society). A decision-theoretic analysis shows that all strategies except approving of a least-preferred candidate are undominated, so voters will often find it optimal to approve of more than one candidate. In party-list systems, SAV apportions seats to parties according to the Jefferson/d’Hondt method with a quota constraint, which favors large parties and gives an incentive to smaller parties to coordinate their policies and forge alliances, even before an election, that reflect their supporters’ coalitional preferences.

Keywords: multiwinner election, voting, approval ballot, proportional representation, apportionment, Game Theory Society

JEL Classification: C70, D2, D7

Suggested Citation

Brams, Steven and Kilgour, D. Marc, Satisfaction Approval Voting (April 14, 2010). Available at SSRN: or

Steven Brams (Contact Author)

New York University (NYU) - Wilf Family Department of Politics ( email )

Dept. of Politics
19 West 4th St., 2nd Fl.
New York, NY 10012
United States
212-998-8510 (Phone)
212-995-4184 (Fax)


D. Marc Kilgour

Wilfrid Laurier University ( email )

75 University Ave W
Waterloo, Ontario N2L 3C5
519-884-0710 Ext.4208 (Phone)
519-884-5057 (Fax)

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