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Experiments with Kemeny ranking: What works when?

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  • Ali, Alnur
  • Meilă, Marina

Abstract

This paper performs a comparison of several methods for Kemeny rank aggregation (104 algorithms and combinations thereof in total) originating in social choice theory, machine learning, and theoretical computer science, with the goal of establishing the best trade-offs between search time and performance. We find that, for this theoretically NP-hard task, in practice the problems span three regimes: strong consensus, weak consensus, and no consensus. We make specific recommendations for each, and propose a computationally fast test to distinguish between the regimes.

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  • Ali, Alnur & Meilă, Marina, 2012. "Experiments with Kemeny ranking: What works when?," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 28-40.
    • Handle: RePEc:eee:matsoc:v:64:y:2012:i:1:p:28-40
    DOI: 10.1016/j.mathsocsci.2011.08.008
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    References listed on IDEAS

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    1. R. L. Plackett, 1975. "The Analysis of Permutations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(2), pages 193-202, June.
    2. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
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    Cited by:

    1. 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.
    2. Kateri, Maria & Nikolov, Nikolay I., 2022. "A generalized Mallows model based on ϕ-divergence measures," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    3. Irurozki, Ekhine & Calvo, Borja & Lozano, Jose A., 2016. "PerMallows: An R Package for Mallows and Generalized Mallows Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i12).
    4. Kiatsupaibul, Seksan & J. Hayter, Anthony & Liu, Wei, 2017. "Rank constrained distribution and moment computations," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 229-242.
    5. Yangming Zhou & Jin-Kao Hao & Zhen Li, 2024. "Heuristic Search for Rank Aggregation with Application to Label Ranking," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 308-326, March.
    6. Srikanth Jagabathula & Paat Rusmevichientong, 2017. "Nonparametric Joint Assortment and Price Choice Model," Management Science, INFORMS, vol. 63(9), pages 3128-3145, September.
    7. Bernard Monjardet, 2013. "Marc Barbut au pays des médianes," Documents de travail du Centre d'Economie de la Sorbonne 13039, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    8. Jansen, C. & Schollmeyer, G. & Augustin, T., 2018. "A probabilistic evaluation framework for preference aggregation reflecting group homogeneity," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 49-62.
    9. Srikanth Jagabathula & Gustavo Vulcano, 2018. "A Partial-Order-Based Model to Estimate Individual Preferences Using Panel Data," Management Science, INFORMS, vol. 64(4), pages 1609-1628, April.
    10. 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.
    11. Aledo, Juan A. & Gámez, Jose A. & Molina, David, 2016. "Using extension sets to aggregate partial rankings in a flexible setting," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 208-223.
    12. 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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