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Axiomatic aggregation of incomplete rankings

Author

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  • Erick Moreno-Centeno
  • Adolfo R. Escobedo

Abstract

In many different applications of group decision-making, individual ranking agents or judges are able to rank only a small subset of all available candidates. However, as we argue in this article, the aggregation of these incomplete ordinal rankings into a group consensus has not been adequately addressed. We propose an axiomatic method to aggregate a set of incomplete rankings into a consensus ranking; the method is a generalization of an existing approach to aggregate complete rankings. More specifically, we introduce a set of natural axioms that must be satisfied by a distance between two incomplete rankings; prove the uniqueness and existence of a distance satisfying such axioms; formulate the aggregation of incomplete rankings as an optimization problem; propose and test a specific algorithm to solve a variation of this problem where the consensus ranking does not contain ties; and show that the consensus ranking obtained by our axiomatic approach is more intuitive than the consensus ranking obtained by other approaches.

Suggested Citation

  • Erick Moreno-Centeno & Adolfo R. Escobedo, 2016. "Axiomatic aggregation of incomplete rankings," IISE Transactions, Taylor & Francis Journals, vol. 48(6), pages 475-488, June.
    • Handle: RePEc:taf:uiiexx:v:48:y:2016:i:6:p:475-488
    DOI: 10.1080/0740817X.2015.1109737
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    Citations

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    Cited by:

    1. Francisco Salas-Molina & Filippo Bistaffa & Juan A. Rodriguez-Aguilar, 2024. "A General Approach for Computing a Consensus in Group Decision Making That Integrates Multiple Ethical Principles," Papers 2401.07818, arXiv.org, revised Mar 2024.
    2. Akbari, Sina & Escobedo, Adolfo R., 2023. "Beyond kemeny rank aggregation: A parameterizable-penalty framework for robust ranking aggregation with ties," Omega, Elsevier, vol. 119(C).
    3. Francisco Pedroche & J. Alberto Conejero, 2020. "Corrected Evolutive Kendall’s τ Coefficients for Incomplete Rankings with Ties: Application to Case of Spotify Lists," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
    4. Hiroki Nishimura & Efe A. Ok, 2022. "A class of dissimilarity semimetrics for preference relations," Papers 2203.04418, arXiv.org.
    5. Fu, Yelin & Lu, Yihe & Yu, Chen & Lai, Kin Keung, 2022. "Inter-country comparisons of energy system performance with the energy trilemma index: An ensemble ranking methodology based on the half-quadratic theory," Energy, Elsevier, vol. 261(PA).
    6. Yeawon Yoo & Adolfo R. Escobedo, 2021. "A New Binary Programming Formulation and Social Choice Property for Kemeny Rank Aggregation," Decision Analysis, INFORMS, vol. 18(4), pages 296-320, December.
    7. Li, Ying & Liu, Peide & Li, Gang, 2023. "An asymmetric cost consensus based failure mode and effect analysis method with personalized risk attitude information," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    8. Yucheng Dong & Yao Li & Ying He & Xia Chen, 2021. "Preference–Approval Structures in Group Decision Making: Axiomatic Distance and Aggregation," Decision Analysis, INFORMS, vol. 18(4), pages 273-295, December.
    9. Salas-Molina, Francisco & Bistaffa, Filippo & Rodríguez-Aguilar, Juan A., 2023. "A general approach for computing a consensus in group decision making that integrates multiple ethical principles," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    10. Youssef Allouah & Rachid Guerraoui & L^e-Nguy^en Hoang & Oscar Villemaud, 2022. "Robust Sparse Voting," Papers 2202.08656, arXiv.org, revised Jan 2024.
    11. Yoo, Yeawon & Escobedo, Adolfo R. & Skolfield, J. Kyle, 2020. "A new correlation coefficient for comparing and aggregating non-strict and incomplete rankings," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1025-1041.

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