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Reducing the Computational Time for the Kemeny Method by Exploiting Condorcet Properties

Author

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  • Noelia Rico

    (Department of Computer Science, University of Oviedo, 33203 Gijón, Spain)

  • Camino R. Vela

    (Department of Computer Science, University of Oviedo, 33203 Gijón, Spain)

  • Raúl Pérez-Fernández

    (Department of Statistics and O.R. and Mathematics Didactics, University of Oviedo, 33007 Oviedo, Spain)

  • Irene Díaz

    (Department of Computer Science, University of Oviedo, 33203 Gijón, Spain)

Abstract

Preference aggregation and in particular ranking aggregation are mainly studied by the field of social choice theory but extensively applied in a variety of contexts. Among the most prominent methods for ranking aggregation, the Kemeny method has been proved to be the only one that satisfies some desirable properties such as neutrality, consistency and the Condorcet condition at the same time. Unfortunately, the problem of finding a Kemeny ranking is NP-hard, which prevents practitioners from using it in real-life problems. The state of the art of exact algorithms for the computation of the Kemeny ranking experienced a major boost last year with the presentation of an algorithm that provides searching time guarantee up to 13 alternatives. In this work, we propose an enhanced version of this algorithm based on pruning the search space when some Condorcet properties hold. This enhanced version greatly improves the performance in terms of runtime consumption.

Suggested Citation

  • Noelia Rico & Camino R. Vela & Raúl Pérez-Fernández & Irene Díaz, 2021. "Reducing the Computational Time for the Kemeny Method by Exploiting Condorcet Properties," Mathematics, MDPI, vol. 9(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1380-:d:574921
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    References listed on IDEAS

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    1. Gaertner, Wulf, 2009. "A Primer in Social Choice Theory: Revised Edition," OUP Catalogue, Oxford University Press, number 9780199565306.
    2. Azzini, Ivano & Munda, Giuseppe, 2020. "A new approach for identifying the Kemeny median ranking," European Journal of Operational Research, Elsevier, vol. 281(2), pages 388-401.
    3. Young, H. P., 1988. "Condorcet's Theory of Voting," American Political Science Review, Cambridge University Press, vol. 82(4), pages 1231-1244, December.
    4. Ali, Alnur & Meilă, Marina, 2012. "Experiments with Kemeny ranking: What works when?," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 28-40.
    5. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, April.
    6. Amodio, S. & D’Ambrosio, A. & Siciliano, R., 2016. "Accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the Kemeny axiomatic approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 667-676.
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    Cited by:

    1. Pedro García-del-Valle-y-Durán & Eduardo Gamaliel Hernandez-Martinez & Guillermo Fernández-Anaya, 2022. "The Greatest Common Decision Maker: A Novel Conflict and Consensus Analysis Compared with Other Voting Procedures," Mathematics, MDPI, vol. 10(20), pages 1-39, October.
    2. Rico, Noelia & Vela, Camino R. & Díaz, Irene, 2023. "Reducing the time required to find the Kemeny ranking by exploiting a necessary condition for being a winner," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1323-1336.

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