Matrix representation of consensus and dissent stabilities in the graph model for conflict resolution

Abstract

The matrix representations of consensus or dissent stabilities for two decision makers are developed under the framework of the graph model for conflict resolution. This explicit algebraic form can be more effectively and conveniently employed to calculate consensus or dissent stabilities and predict equilibria of a graph model, while also facilitating modifications and new extensions. More specifically, this paper presents and proves the matrix definitions of eight stabilities considering the consensual and dissensual behaviors of decision makers. Then these stability concepts within the consensus and dissent preference are embedded into the latest version of decision support system NUAAGMCR, which can be used to study real-world conflicts. Through an illustrative case study, the procedure of applying the proposed algebraic method for calculating stability concepts in regard to consensus and dissent preferences is demonstrated, and valuable strategic insights are provided for a better understanding of the decision makers’ behaviors.