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The Greatest Common Decision Maker: A Novel Conflict and Consensus Analysis Compared with Other Voting Procedures

Author

Listed:
  • Pedro García-del-Valle-y-Durán

    (Department of Physics and Mathematics, Universidad Iberoamericana Ciudad de Mexico, Mexico City C.P. 01219, Mexico)

  • Eduardo Gamaliel Hernandez-Martinez

    (Institute of Applied Research and Technology (INIAT), Universidad Iberoamericana Ciudad de Mexico, Mexico City C.P. 01219, Mexico)

  • Guillermo Fernández-Anaya

    (Department of Physics and Mathematics, Universidad Iberoamericana Ciudad de Mexico, Mexico City C.P. 01219, Mexico)

Abstract

Consensus or conflict agreements, and how these change over time, have significant consequences for understanding the network behavior of human beings, especially when it is necessary to have agreements to move companies and countries forward peacefully. This paper proposes a new Greatest Common Decision Maker (GCDM) aggregation voting procedure applied to square preference matrices of n alternatives and n decision makers. An analysis of the mathematical combinatory ranking of consensus and conflicts generated by the GCDM is realized, and compared to the well-known Borda, Pluralism and Condorcet aggregation procedures to cover the entire class of dynamic accountable group decision-making phenomena. A classification for the family of magic squares is reviewed and it is determined that a conflict decision matrix corresponds to a Latin square. As an original contribution, a 2D color heatmap is generated as a visual tool to compare the consensus and conflict cases generated by the compared methods. Finally, a new consensus reaching model is proposed to compare these aggregation methods defining cost and effort change matrices to convert the cases of conflicts into consensus according to the change in individual preferences. The incorporation of social concepts into our research makes the results obtained stronger.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3815-:d:943715
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    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. Gong, Zaiwu & Zhang, Huanhuan & Forrest, Jeffrey & Li, Lianshui & Xu, Xiaoxia, 2015. "Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual," European Journal of Operational Research, Elsevier, vol. 240(1), pages 183-192.
    3. 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.
    4. 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.
    5. Mahajne, Muhammad & Volij, Oscar, 2022. "Pairwise consensus and the Borda rule," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 17-21.
    6. Peter Emerson, 2013. "The original Borda count and partial voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 353-358, February.
    7. Ruben Heradio & David Fernandez-Amoros & Cristina Cerrada & Manuel J. Cobo, 2020. "Group Decision-Making Based on Artificial Intelligence: A Bibliometric Analysis," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    8. Kai An Sim & Kok Bin Wong, 2021. "Magic Square and Arrangement of Consecutive Integers That Avoids k -Term Arithmetic Progressions," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    9. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
    10. Wilkinson, Leland & Friendly, Michael, 2009. "The History of the Cluster Heat Map," The American Statistician, American Statistical Association, vol. 63(2), pages 179-184.
    11. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    12. Keiichi Morimoto, 2021. "Information Use and the Condorcet Jury Theorem," Mathematics, MDPI, vol. 9(10), pages 1-22, May.
    13. Smith,Samuel Bruce, 2015. "Chance, Strategy, and Choice," Cambridge Books, Cambridge University Press, number 9781107084520, September.
    14. Zhang, Hengjie & Dong, Yucheng & Chiclana, Francisco & Yu, Shui, 2019. "Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design," European Journal of Operational Research, Elsevier, vol. 275(2), pages 580-598.
    15. Yuanming Li & Ying Ji & Shaojian Qu, 2022. "Consensus Building for Uncertain Large-Scale Group Decision-Making Based on the Clustering Algorithm and Robust Discrete Optimization," Group Decision and Negotiation, Springer, vol. 31(2), pages 453-489, April.
    16. Paul H. Edelman, 2015. "The Myth of the Condorcet Winner," Supreme Court Economic Review, University of Chicago Press, vol. 22(1), pages 207-219.
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