Clusterability of groups and information exchange in group decision making with approval voting system

In this paper, we discuss the relations between clusterability of a group and information exchange in a situation of decision making of the group. Based on the equivalence of clusterability to Newcomb's stability of sentiments, we show that the concept of interaction consistency of a group that is involved in a decision making situation of selecting a set of representatives of the group from the members of the group, the concept that is newly proposed in this paper, is equivalent to the clusterability of the group. Moreover, we propose the concept of quasi-clusterability of a group, the concept that is a generalization of the concept of clusterability of a group, and show that the interaction consistency of a group that is involved in a decision making situation of selecting a set of representatives of the group from a set of candidates, each of which is a member of the group, is equivalent to the quasi-clusterability of the group.