IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i20p3815-d943715.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/20/3815/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/20/3815/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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, October.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. González-Arteaga, T. & Alcantud, J.C.R. & de Andrés Calle, R., 2016. "A cardinal dissensus measure based on the Mahalanobis distance," European Journal of Operational Research, Elsevier, vol. 251(2), pages 575-585.
    2. 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).
    3. Zhang, Bowen & Dong, Yucheng & Zhang, Hengjie & Pedrycz, Witold, 2020. "Consensus mechanism with maximum-return modifications and minimum-cost feedback: A perspective of game theory," European Journal of Operational Research, Elsevier, vol. 287(2), pages 546-559.
    4. Labella, Álvaro & Liu, Hongbin & Rodríguez, Rosa M. & Martínez, Luis, 2020. "A Cost Consensus Metric for Consensus Reaching Processes based on a comprehensive minimum cost model," European Journal of Operational Research, Elsevier, vol. 281(2), pages 316-331.
    5. Xiangrui Chao & Yucheng Dong & Gang Kou & Yi Peng, 2022. "How to determine the consensus threshold in group decision making: a method based on efficiency benchmark using benefit and cost insight," Annals of Operations Research, Springer, vol. 316(1), pages 143-177, September.
    6. Zhen Zhang & Zhuolin Li, 2023. "Consensus-based TOPSIS-Sort-B for multi-criteria sorting in the context of group decision-making," Annals of Operations Research, Springer, vol. 325(2), pages 911-938, June.
    7. Zhang, Hengjie & Dong, Yucheng & Xiao, Jing & Chiclana, Francisco & Herrera-Viedma, Enrique, 2021. "Consensus and opinion evolution-based failure mode and effect analysis approach for reliability management in social network and uncertainty contexts," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    8. Cheng, Dong & Yuan, Yuxiang & Wu, Yong & Hao, Tiantian & Cheng, Faxin, 2022. "Maximum satisfaction consensus with budget constraints considering individual tolerance and compromise limit behaviors," European Journal of Operational Research, Elsevier, vol. 297(1), pages 221-238.
    9. García-Zamora, Diego & Dutta, Bapi & Massanet, Sebastia & Riera, Juan Vicente & Martínez, Luis, 2023. "Relationship between the distance consensus and the consensus degree in comprehensive minimum cost consensus models: A polytope-based analysis," European Journal of Operational Research, Elsevier, vol. 306(2), pages 764-776.
    10. Michel Truchon, 2005. "Aggregation of Rankings: a Brief Review of Distance-Based Rules," Cahiers de recherche 0534, CIRPEE.
    11. Meng, Fan-Yong & Gong, Zai-Wu & Pedrycz, Witold & Chu, Jun-Fei, 2023. "Selfish-dilemma consensus analysis for group decision making in the perspective of cooperative game theory," European Journal of Operational Research, Elsevier, vol. 308(1), pages 290-305.
    12. Guo, Weiwei & Gong, Zaiwu & Zhang, Wei-Guo & Xu, Yanxin, 2023. "Minimum cost consensus modeling under dynamic feedback regulation mechanism considering consensus principle and tolerance level," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1279-1295.
    13. Miriam Aparicio, 2021. "Resiliency and Cooperation or Regarding Social and Collective Competencies for University Achievement. An Analysis from a Systemic Perspective," European Journal of Social Sciences Education and Research Articles, Revistia Research and Publishing, vol. 8, ejser_v8_.
    14. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    15. Fabio Salamanca-Buentello & Mary V Seeman & Abdallah S Daar & Ross E G Upshur, 2020. "The ethical, social, and cultural dimensions of screening for mental health in children and adolescents of the developing world," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-25, August.
    16. Mónica de Castro-Pardo & Fernando Pérez-Rodríguez & José María Martín-Martín & João C. Azevedo, 2019. "Planning for Democracy in Protected Rural Areas: Application of a Voting Method in a Spanish-Portuguese Reserve," Land, MDPI, vol. 8(10), pages 1-17, October.
    17. Tuba Bircan & Almila Alkim Akdag Salah, 2022. "A Bibliometric Analysis of the Use of Artificial Intelligence Technologies for Social Sciences," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
    18. Nicodemo, Catia & Satorra, Albert, 2020. "Exploratory Data Analysis on Large Data Sets: The Example of Salary Variation in Spanish Social Security Data," IZA Discussion Papers 13459, Institute of Labor Economics (IZA).
    19. Rodríguez Alcantud, José Carlos & de Andrés Calle, Rocío & González-Arteaga, Teresa, 2013. "Codifications of complete preorders that are compatible with Mahalanobis disconsensus measures," MPRA Paper 50533, University Library of Munich, Germany.
    20. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3815-:d:943715. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.