In this paper, treating situations of group decision making with interperce
ption by decision makers, we provide two propositions that are related to a
voiding time-consuming events in the situations. Regarding a meeting with o
dd number of decision makers and majority rule, one shows that if it is ins
ide common knowledge among the decision makers that their emotions are stab
le, then it cannot be inside common knowledge that the meeting is in a dead
lock. Another implies that if the decision makers believes that their emoti
ons are stable, then there exists a decision maker who believes that the me
eting is not in a deadlock. We can see from these propositions that stabili
ty of decision makers' emotions plays important role in smooth progress of
a meeting, even if the meeting is with incomplete information. (C) 2000 Els
evier Science Inc. All rights reserved.