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An iterative approach for achieving consensus when ranking a finite set of alternatives by a group of experts

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  • Hou, Fujun
  • Triantaphyllou, Evangelos

Abstract

This paper proposes a novel iterative approach for achieving consensus when a group of experts is given the task to rank a finite set of alternatives. Unlike traditional approaches which use various metrics to express expert disagreements, the proposed approach is based on a premetric concept to express such disagreements. This premetric approach can capture more effectively the nature of agreements or disagreements that naturally occur when experts rank alternatives. The proposed approach is very flexible in that it considers a wide spectrum of ways to approach the problem of reaching consensus. These ways are based on an assignment formulation where one may consider various alternative consensus improving strategies. Which strategy to consider depends on the nature of the group decision making (GDM) problem under consideration and it can change as the GDM process evolves. In particular, this paper examines and provides novel solutions for the following fundamental problems: (1) How to evaluate the level of consensus? (2) How to identify the most appropriate disagreements to consider next when the consensus is not at a desired level? and (3) How to derive a reasonably ’close’ solution when experts are not in perfect consensus while they are not able or not willing to further improve the consensus? Furthermore, this paper provides a theoretical foundation of the proposed premetric-based approach and then it uses this theoretical foundation to compare the new approach with some traditional ones.

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  • Hou, Fujun & Triantaphyllou, Evangelos, 2019. "An iterative approach for achieving consensus when ranking a finite set of alternatives by a group of experts," European Journal of Operational Research, Elsevier, vol. 275(2), pages 570-579.
    • Handle: RePEc:eee:ejores:v:275:y:2019:i:2:p:570-579
    DOI: 10.1016/j.ejor.2018.11.047
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    References listed on IDEAS

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    1. Fujun Hou, 2016. "The Prametric-Based GDM Procedure Under Fuzzy Environment," Group Decision and Negotiation, Springer, vol. 25(5), pages 1071-1084, September.
    2. Alpern, Steve & Chen, Bo, 2017. "The importance of voting order for jury decisions by sequential majority voting," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1072-1081.
    3. Ray, Thomas G. & Triantaphyllou, Evangelos, 1998. "Evaluation of rankings with regard to the possible number of agreements and conflicts," European Journal of Operational Research, Elsevier, vol. 106(1), pages 129-136, April.
    4. Čaklović, Lavoslav & Kurdija, Adrian Satja, 2017. "A universal voting system based on the Potential Method," European Journal of Operational Research, Elsevier, vol. 259(2), pages 677-688.
    5. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    6. Cook, Wade D., 2006. "Distance-based and ad hoc consensus models in ordinal preference ranking," European Journal of Operational Research, Elsevier, vol. 172(2), pages 369-385, July.
    7. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2018. "On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application," European Journal of Operational Research, Elsevier, vol. 271(1), pages 120-140.
    8. Ronald D. Armstrong & Wade D. Cook & Lawrence M. Seiford, 1982. "Priority Ranking and Consensus Formation: The Case of Ties," Management Science, INFORMS, vol. 28(6), pages 638-645, June.
    9. Fujun Hou, 2015. "A Consensus Gap Indicator and Its Application to Group Decision Making," Group Decision and Negotiation, Springer, vol. 24(3), pages 415-428, May.
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    Citations

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    Cited by:

    1. Fujun Hou, 2022. "Conditions for none to be whipped by `Rank and Yank' under the majority rule," Papers 2208.05093, arXiv.org.
    2. Tiantian Gai & Mingshuo Cao & Francisco Chiclana & Zhen Zhang & Yucheng Dong & Enrique Herrera-Viedma & Jian Wu, 2023. "Consensus-trust Driven Bidirectional Feedback Mechanism for Improving Consensus in Social Network Large-group Decision Making," Group Decision and Negotiation, Springer, vol. 32(1), pages 45-74, February.
    3. 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.
    4. Gong, Zaiwu & Guo, Weiwei & Słowiński, Roman, 2021. "Transaction and interaction behavior-based consensus model and its application to optimal carbon emission reduction," Omega, Elsevier, vol. 104(C).
    5. Fujun Hou, 2022. "Reformulating the Value Restriction and the Not-Strict Value Restriction in Terms of Possibility Preference Map," Papers 2205.07400, arXiv.org.
    6. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.
    7. Evangelos Triantaphyllou & Fujun Hou & Juri Yanase, 2020. "Analysis of the Final Ranking Decisions Made by Experts After a Consensus has Been Reached in Group Decision Making," Group Decision and Negotiation, Springer, vol. 29(2), pages 271-291, April.
    8. Fujun Hou, 2022. "Describing Sen's Transitivity Condition in Inequalities and Equations," Papers 2204.05105, arXiv.org.
    9. Triantaphyllou, Evangelos & Yanase, Juri & Hou, Fujun, 2020. "Post-consensus analysis of group decision making processes by means of a graph theoretic and an association rules mining approach," Omega, Elsevier, vol. 94(C).
    10. Fujun Hou, 2018. "Mutual Conversion Between Preference Maps And Cook-Seiford Vectors," Papers 1812.03566, arXiv.org.

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