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

Pedro García-del-Valle-y-Durán, Eduardo Gamaliel Hernandez-Martinez and Guillermo Fernández-Anaya ()
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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

Mathematics, 2022, vol. 10, issue 20, 1-39

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.

Keywords: multi-agent consensus; preference aggregation profile; Borda voting procedures; pluralism voting procedures; greatest common decision; Condorcet voting procedures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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