Limit state analysis on the un-repeated multiple selection bounded confidence model

In this paper, we study the opinion evolution over social networks with a bounded confidence rule. Node initial opinions are independently and identically distributed. At each time step, each node reviews the average opinions of several different randomly selected agents and updates its opinion only when the difference between its opinion and the average is below a threshold. First of all, we provide probability bounds of the opinion convergence and the opinion consensus, are both nontrivial events by analyzing the probability distribution of order statistics. Next, similar analyzing methods are used to provide probability bounds when the selection cover all agents. Finally, we simulate all these bounds and find that opinion fluctuations may take place. These results increase to the understanding of the role of bounded confidence in social opinion dynamics, and the possibility of fluctuation reveals that our model has fundamentally changed the behavior of general DeGroot opinion dynamical processes.