Consensus building and the Graph Model for Conflict Resolution

Consensus building in group decision situations is analyzed within the framework of the Graph Model for Conflict Resolution (GMCR). A group decision situation and consensus in the situation are treated in a mathematical framework for the analysis of committees with permissible ranges of decision makers, and stability and unstability of consensus and non-consensus states are examined within the framework of the GMCR. Consequently, the followings are verified: i) all consensus states are Nash stable for all DMs; ii) the state in which each DM agrees only to his/her best alternative is a non-consensus state and is Nash stable for all DMs, but unstable for all DMs with respect to coalition Nash stability; iii) each of the other non-consensus states is not sequentially stable for at least one DM. Then, some insights on the processes for achieving consensus in group decision situations are provided.