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Achieving fully proportional representation by clustering voters

Author

Listed:
  • Piotr Faliszewski

    (AGH University)

  • Arkadii Slinko

    (University of Auckland)

  • Kolja Stahl

    (TU Berlin)

  • Nimrod Talmon

    (Ben-Gurion University)

Abstract

Both the Chamberlin–Courant and Monroe rules are voting rules that solve the problem of fully proportional representation: given a set of candidates and a set of voters, they select committees of candidates whose members represent the voters so that the voters’ total dissatisfaction is minimized. These two rules suffer from a common disadvantage, namely being computationally intractable. As both the Chamberlin–Courant and Monroe rules, explicitly or implicitly, partition voters so that the voters in each part share the same representative, they can be seen as clustering algorithms. This suggests studying approximation algorithms for these voting rules by means of cluster analysis, which is the subject of this paper. Using ideas from cluster analysis we develop several approximation algorithms for the Chamberlin–Courant and Monroe rules and experimentally analyze their performance. We find that our algorithms are computationally efficient and, in many cases, are able to provide solutions which are very close to optimal.

Suggested Citation

  • Piotr Faliszewski & Arkadii Slinko & Kolja Stahl & Nimrod Talmon, 2018. "Achieving fully proportional representation by clustering voters," Journal of Heuristics, Springer, vol. 24(5), pages 725-756, October.
    • Handle: RePEc:spr:joheur:v:24:y:2018:i:5:d:10.1007_s10732-018-9376-y
    DOI: 10.1007/s10732-018-9376-y
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    References listed on IDEAS

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    1. Monroe, Burt L., 1995. "Fully Proportional Representation," American Political Science Review, Cambridge University Press, vol. 89(4), pages 925-940, December.
    2. Ariel Procaccia & Jeffrey Rosenschein & Aviv Zohar, 2008. "On the complexity of achieving proportional representation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 353-362, April.
    3. John C. McCabe-Dansted & Arkadii Slinko, 2006. "Exploratory Analysis of Similarities Between Social Choice Rules," Group Decision and Negotiation, Springer, vol. 15(1), pages 77-107, January.
    4. 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.
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