Characterizing the process of reaching consensus for social systems

A novel way of characterizing the process of reaching consensus for a social system is given. The foundation of the characterization is based on the theorem which states that the sufficient and necessary condition for a system to reach the state of consensus is the occurrence of communicators, defined as the units of the system that can directly communicate with all the others simultaneously. A model is proposed to illustrate the characterization explicitly. The existence of communicators provides an efficient way for unifying two systems that a state of consensus is guaranteed after the mergence.