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A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights

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  • Ignacio Contreras

    (University Pablo de Olavide)

Abstract

In this paper we propose a preference aggregation procedure for those cases in which the decision-makers express their preferences by means of a ranking of alternatives. Among the most applied methods for this purpose are those inspired by the Borda–Kendall rule, which attach to each alternative an aggregated value of the votes received in the different rank positions, and those based on distance measures between individual and collective preferences, which look for the solution that maximizes the consensus. The main idea here is to integrate these two approaches. Taking into account that the information about the values of weights or utilities assigned to each rank position is imprecise, we propose an evaluation of the alternatives using that vector of weights that minimizes the disagreement between DMs. In order to solve the problem, mixed-integer linear programming models are constructed. Two numerical examples are examined to illustrate the applicability of the proposed procedure.

Suggested Citation

  • Ignacio Contreras, 2010. "A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights," Group Decision and Negotiation, Springer, vol. 19(5), pages 441-456, September.
    • Handle: RePEc:spr:grdene:v:19:y:2010:i:5:d:10.1007_s10726-008-9127-9
    DOI: 10.1007/s10726-008-9127-9
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    References listed on IDEAS

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    1. Duncan Black, 1976. "Partial justification of the Borda count," Public Choice, Springer, vol. 28(1), pages 1-15, December.
    2. Wade D. Cook & Lawrence M. Seiford, 1982. "On the Borda-Kendall Consensus Method for Priority Ranking Problems," Management Science, INFORMS, vol. 28(6), pages 621-637, June.
    3. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    4. Pavel Yu. Chebotarev & Elena Shamis, 1998. "Characterizations of scoring methodsfor preference aggregation," Annals of Operations Research, Springer, vol. 80(0), pages 299-332, January.
    5. Foroughi, A.A. & Tamiz, M., 2005. "An effective total ranking model for a ranked voting system," Omega, Elsevier, vol. 33(6), pages 491-496, December.
    6. Wade D. Cook & Moshe Kress, 1990. "A Data Envelopment Model for Aggregating Preference Rankings," Management Science, INFORMS, vol. 36(11), pages 1302-1310, November.
    7. Cook, Wade D. & Kress, Moshe & Seiford, Lawrence M., 1997. "A general framework for distance-based consensus in ordinal ranking models," European Journal of Operational Research, Elsevier, vol. 96(2), pages 392-397, January.
    8. Hannu Nurmi, 2004. "A Comparison of Some Distance-Based Choice Rules in Ranking Environments," Theory and Decision, Springer, vol. 57(1), pages 5-24, August.
    9. González-Pachøn, Jacinto & Romero, Carlos, 1999. "Distance-based consensus methods: a goal programming approach," Omega, Elsevier, vol. 27(3), pages 341-347, June.
    10. Daniel Eckert & Christian Klamler & Johann Mitlöhner & Christian Schlötterer, 2006. "A distance-based comparison of basic voting rules," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(4), pages 377-386, December.
    11. Obata, Tsuneshi & Ishii, Hiroaki, 2003. "A method for discriminating efficient candidates with ranked voting data," European Journal of Operational Research, Elsevier, vol. 151(1), pages 233-237, November.
    12. Donald G. Saari & Vincent R. Merlin, 2000. "A geometric examination of Kemeny's rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 403-438.
    13. Hashimoto, Akihiro, 1997. "A ranked voting system using a DEA/AR exclusion model: A note," European Journal of Operational Research, Elsevier, vol. 97(3), pages 600-604, March.
    14. Cook, Wade D. & Kress, Moshe, 1986. "Ordinal ranking and preference strength," Mathematical Social Sciences, Elsevier, vol. 11(3), pages 295-306, June.
    15. Wade D. Cook & Moshe Kress, 1985. "Ordinal Ranking with Intensity of Preference," Management Science, INFORMS, vol. 31(1), pages 26-32, January.
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    Cited by:

    1. Zhibin Wu & Jie Xiao & Ivan Palomares, 2019. "Direct Iterative Procedures for Consensus Building with Additive Preference Relations Based on the Discrete Assessment Scale," Group Decision and Negotiation, Springer, vol. 28(6), pages 1167-1191, December.
    2. Jiuping Xu & Zhibin Wu & Yuan Zhang, 2014. "A Consensus Based Method for Multi-criteria Group Decision Making Under Uncertain Linguistic Setting," Group Decision and Negotiation, Springer, vol. 23(1), pages 127-148, January.
    3. Lozano-Oyola, Macarena & Contreras, Ignacio & Blancas, Francisco Javier, 2019. "An Operational Non-compensatory Composite Indicator: Measuring Sustainable Tourism in Andalusian Urban Destinations," Ecological Economics, Elsevier, vol. 159(C), pages 1-10.
    4. Amin Mahmoudi & Saad Ahmed Javed, 2023. "Uncertainty Analysis in Group Decisions through Interval Ordinal Priority Approach," Group Decision and Negotiation, Springer, vol. 32(4), pages 807-833, August.
    5. Bowen Zhang & Yucheng Dong & Enrique Herrera-Viedma, 2019. "Group Decision Making with Heterogeneous Preference Structures: An Automatic Mechanism to Support Consensus Reaching," Group Decision and Negotiation, Springer, vol. 28(3), pages 585-617, June.
    6. Xiang Deng & Xiang Cheng & Jing Gu & Zeshui Xu, 2021. "An Innovative Indicator System and Group Decision Framework for Assessing Sustainable Development Enterprises," Group Decision and Negotiation, Springer, vol. 30(6), pages 1201-1238, December.
    7. I. Contreras, 2012. "Ordered Weighted Disagreement Functions," Group Decision and Negotiation, Springer, vol. 21(3), pages 345-361, May.

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