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Multi winner Approval Voting: An Apportionment Approach

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Listed:
  • Brams, Steven J.
  • Kilgour, D. Marc
  • Potthoff, Richard F.

Abstract

We extend approval voting so as to elect multiple candidates, who may be either individuals or members of a political party, in rough proportion to their approval in the electorate. We analyze two divisor methods of apportionment, first proposed by Jefferson and Webster, that iteratively depreciate the approval votes of voters who have one or more of their approved candidates already elected. We compare the usual sequential version of these methods with a nonsequential version, which is computationally complex but feasible for many elections. Whereas Webster apportionments tend to be more representative of the electorate than those of Jefferson, the latter, whose equally spaced vote thresholds for winning seats duplicate those of cumulative voting in 2-party elections, is even-handed or balanced.

Suggested Citation

  • Brams, Steven J. & Kilgour, D. Marc & Potthoff, Richard F., 2017. "Multi winner Approval Voting: An Apportionment Approach," MPRA Paper 77931, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:77931
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    References listed on IDEAS

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    1. Dan S. Felsenthal & Moshé Machover (ed.), 2012. "Electoral Systems," Studies in Choice and Welfare, Springer, number 978-3-642-20441-8, December.
    2. 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.
    3. Markus Brill & Jean-François Laslier & Piotr Skowron, 2018. "Multiwinner approval rules as apportionment methods," Journal of Theoretical Politics, , vol. 30(3), pages 358-382, July.
    4. Steven J. Brams & Markus Brill & Anne-Marie George, 2022. "The excess method: a multiwinner approval voting procedure to allocate wasted votes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 283-300, February.
    5. Haris Aziz & Markus Brill & Vincent Conitzer & Edith Elkind & Rupert Freeman & Toby Walsh, 2017. "Justified representation in approval-based committee voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 461-485, February.
    6. Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
    7. Steven J. Brams, 1990. "Constrained Approval Voting: A Voting System to Elect a Governing Board," Interfaces, INFORMS, vol. 20(5), pages 67-80, October.
    8. 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.
    9. Edith Elkind & Piotr Faliszewski & Piotr Skowron & Arkadii Slinko, 2017. "Properties of multiwinner voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 599-632, March.
    10. Brams, Steven J. & Fishburn, Peter C., 1978. "Approval Voting," American Political Science Review, Cambridge University Press, vol. 72(3), pages 831-847, September.
    11. Subiza, Begoña & Peris, Josep E., 2014. "A Consensual Committee Using Approval Balloting," QM&ET Working Papers 14-5, University of Alicante, D. Quantitative Methods and Economic Theory.
    12. Monroe, Burt L., 1995. "Fully Proportional Representation," American Political Science Review, Cambridge University Press, vol. 89(4), pages 925-940, December.
    13. Rosario Laratta (ed.), 2012. "Social Welfare," Books, IntechOpen, number 1876.
    14. Chamberlin, John R. & Courant, Paul N., 1983. "Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule," American Political Science Review, Cambridge University Press, vol. 77(3), pages 718-733, September.
    15. 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.
    16. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, December.
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    Citations

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    Cited by:

    1. Pierre Dehez & Victor Ginsburgh, 2020. "Approval voting and Shapley ranking," Public Choice, Springer, vol. 184(3), pages 415-428, September.
    2. Markus Brill & Jean-François Laslier & Piotr Skowron, 2018. "Multiwinner approval rules as apportionment methods," Journal of Theoretical Politics, , vol. 30(3), pages 358-382, July.
    3. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2020. "On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle," Revue d'économie politique, Dalloz, vol. 130(5), pages 699-725.
    4. Mostapha Diss & Eric Kamwa & Abdelmonaim Tlidi, 2019. "On some k-scoring rules for committee elections: agreement and Condorcet Principle," Working Papers hal-02147735, HAL.
    5. Markus Brill & Paul Gölz & Dominik Peters & Ulrike Schmidt-Kraepelin & Kai Wilker, 2022. "Approval-based apportionment," Post-Print hal-03816043, HAL.
    6. Aaron Hamlin & Whitney Hua, 2023. "The case for approval voting," Constitutional Political Economy, Springer, vol. 34(3), pages 335-345, September.
    7. Steven J. Brams & Markus Brill & Anne-Marie George, 2022. "The excess method: a multiwinner approval voting procedure to allocate wasted votes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 283-300, February.
    8. Arnold Cédrick SOH VOUTSA, 2020. "Approval Voting & Majority Judgment in Weighted Representative Democracy," THEMA Working Papers 2020-15, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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    More about this item

    Keywords

    Approval voting; apportionment methods; multiple winners; proportional representation; cumulative voting;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • D6 - Microeconomics - - Welfare Economics
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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