Satisfaction approval voting

Brams, Steven J and Kilgour, D. Marc (2010): Satisfaction approval voting.

Abstract

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 disjoint—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.

• Item Type: MPRA Paper
• Language: English
• Keywords: multiwinner election; voting system; approval ballot; proportional representation; apportonment
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; D - Microeconomics > D0 - General > D02 - Institutions: Design, Formation, Operations, and Impact; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General

References

Alcalde-Unzu, Jorge, and Marc Vorsatz (2009). “Size Approval Voting.” Journal of Economic Theory 144, no. 3 (May): 1187-1210.

Balinski, M. L., and H. P. Young (1978). “Stability, Coalitions and Schisms in Proportional Representation Systems.” American Political Science Review 72, no. 3 (September): 848-858.

Balinski, Michel L., and H. Peyton Young (1982/2001). Fair Representation: Meeting the Ideal of One Man, One Vote. New Haven, CT/Washington, DC: Yale University Press/Brookings Institution.

Barberà, S., M. Maschler, and J. Shalev (2001). “Voting for Voters: A Model of Electoral Evolution.” Games and Economic Behavior 37, no. 1 (October): 40-78.

Brams, Steven J. (2008). Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures. Princeton, NJ: Princeton University Press.

Brams, Steven J., and Peter C. Fishburn (1978). “Approval Voting.” American Political Science Review 72, no. 3 (September): 831-847.

Brams, Steven J., and Peter C. Fishburn (1983/2007). Approval Voting. New York: Springer.

Brams, Steven J., D. Marc Kilgour, and M. Remzi Sanver (2007). “A Minimax Procedure for Electing Committees.” Public Choice 132, nos. 3-4 (September): 401-420.

Karp, Richard M. (1972). “Reducibility among Combinatorial Problems.” In R. E. Miller and J. W. Thatcher (eds.), Complexity of Computer Calculations. New York: Plenum, pp. 85-103.

Kilgour, D. Marc (2010). “Using Approval Balloting in Multi-Winner Elections.” In Jean-François Laslier and M. Remzi Sanver (eds.), Handbook of Approval Voting. Berlin: Springer.

Merrill, Samuel, III, and Jack H. Nagel (1987). “The Effect of Approval Balloting on Strategic Voting under Alternative Decision Rules.” American Political Science Review 81, no. 2 (June): 509-524.

Still, J. W. (1979). “A Class of New Methods for Congressional Apportionment.” SIAM Journal on Applied Mathematics 37, no. 2 (October): 401-418.