Solution on Tie in Three-Opinion Dynamics Research

Group discussion is an newly important way in discrete dynamic models, we named it Galam models. In each update procession, the population will be divided into groups with a fixed number of members. After discussion, each group will share the same opinion. However, in such away we will encounter a common problem, which is that a tie appears in a group. We can solve the problem in many ways, but one thing we have to consider about is fairness. In this paper, we discuss on two kinds solution. One way is to randomly select one of the opinions in a tie, the other is to select the nearest group´s common opinion. We use simulation tools to simulate these two ways and make comparison based on the simulation results. At last we also study the importance of a opinion´s initial supported rate in order to win the dynamics.