Strength of preference in graph models for multiple-decision-maker conflicts

Models of strength of preference are incorporated into the graph model for conflict resolution to study realistically multi-objective decision making situations in disputes with any finite number of participants. A decision maker’s preference is expressed using a triplet of binary relations that allows preference of one state over another to be strong or weak, and also allows indifference. Four basic stability definitions used in the graph model to represent human behavior in conflicts are extended to the context of the new triplet preference structure, producing strong and weak stabilities. Theorems governing the relationships among standard, strong, and weak stabilities are presented. Finally, application of the new preference representation to an international water resource management conflict confirms the practical utility of the triplet structure and the significance of the strategic insights it can provide.