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Approval elections with a variable number of winners

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  • D. Marc Kilgour

    (Wilfrid Laurier University)

Abstract

Multi-winner elections, for example, the election of members to a committee, are now quite common, and include the interesting subclass of elections with a variable number of winners, or VNW elections. In VNW elections, voters determine how many winners there are, as well as which candidates win. Common VNW elections include elections to bestow honorary status, such as enshrinement in a hall of fame, and elections to determine a shortlist of, say, job candidates for interviews. Such elections are VNW elections whenever the number of winners is not specified in advance. Multi-winner elections are often conducted by adapting standard procedures for single-winner elections. Approval balloting is particularly appropriate for multi-winner elections, as every ballot, and the set of winners, are subsets of the set of all candidates. Many methods of counting approval ballots appropriate to VNW elections are reviewed and illustrated, and their properties—desirable and undesirable—discussed.

Suggested Citation

  • D. Marc Kilgour, 2016. "Approval elections with a variable number of winners," Theory and Decision, Springer, vol. 81(2), pages 199-211, August.
    • Handle: RePEc:kap:theord:v:81:y:2016:i:2:d:10.1007_s11238-016-9535-2
    DOI: 10.1007/s11238-016-9535-2
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    References listed on IDEAS

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    1. Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
    2. Steven J Brams & D Marc Kilgour, 2012. "Narrowing the field in elections: The Next-Two rule," Journal of Theoretical Politics, , vol. 24(4), pages 507-525, October.
    3. Steven J. Brams & D. Marc Kilgour, 2014. "Satisfaction Approval Voting," Studies in Choice and Welfare, in: Rudolf Fara & Dennis Leech & Maurice Salles (ed.), Voting Power and Procedures, edition 127, pages 323-346, Springer.
    4. Thomas Ratliff & Donald Saari, 2014. "Complexities of electing diverse committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 55-71, June.
    5. D. Marc Kilgour & Steven J. Brams & M. Remzi Sanver, 2006. "How to Elect a Representative Committee Using Approval Balloting," Studies in Choice and Welfare, in: Bruno Simeone & Friedrich Pukelsheim (ed.), Mathematics and Democracy, pages 83-95, Springer.
    6. Rudolf Fara & Dennis Leech & Maurice Salles (ed.), 2014. "Voting Power and Procedures," Studies in Choice and Welfare, Springer, edition 127, number 978-3-319-05158-1, December.
    7. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
    8. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
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    Cited by:

    1. Kilgour, D. Marc, 2018. "Multi-Winner Voting/Votación con múltiples ganadores," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 36, pages 167-180, Enero.
    2. Martin Lackner & Jan Maly, 2020. "Approval-Based Shortlisting," Papers 2005.07094, arXiv.org, revised May 2022.
    3. Florian Brandl & Dominik Peters, 2019. "An axiomatic characterization of the Borda mean rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 685-707, April.
    4. Haris Aziz & Sujit Gujar & Manisha Padala & Mashbat Suzuki & Jeremy Vollen, 2022. "Coordinating Monetary Contributions in Participatory Budgeting," Papers 2206.05966, arXiv.org, revised Feb 2023.

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