A complete binary relation to compare coalition influence for social welfare function

This paper proposes a method for comparison of coalition influence in the framework of social welfare function which is a model of group decision. The proposed method compares a pair of coalitions from the point of view how different the opinion which the coalition has with respect to the collective decision is. Some examples how the proposed method work are provided in this paper. It is verified that the binary relation which the proposed method uses is weak order and negatively transitive. A proposition which shows the proposed method satisfies monotonicity which means that a bigger coalition has more power in the group decision. This paper also introduces properties of players and coalitions in the framework of social welfare function. Some relationships between coalition properties and comparison results calculated by the proposed method are provided.