Meetings in deadlock and decision makers with interperception

In this paper, treating situations of group decision making with interperception by decision makers, we provide two propositions that are related to avoiding time-consuming events in the situations. Regarding a meeting with odd number of decision makers and majority rule, one shows that if it is inside common knowledge among the decision makers that their emotions are stable, then it cannot be inside common knowledge that the meeting is in a deadlock. Another implies that if the decision makers believes that their emotions are stable, then there exists a decision maker who believes that the meeting is not in a deadlock. We can see from these propositions that stability of decision makers' emotions plays an important role in smooth progress of a meeting, even if the meeting is with incomplete information.