Fluctuation analysis of a long-range opinion dynamics

In this paper, we propose a bounded-confidence opinion model and focus on the opinion fluctuation resulting from long-range opinion interactions. In this opinion dynamics, there are two stubborn agents that never change their opinions and many regular agents. With different parameters, we demonstrate various opinion phenomena, including agreement and fluctuation, for regular agents that update their opinion using other agents opinion values according to the confidence bound. Moreover, we prove that opinion values of the regular agents fluctuate almost surely if and only if the confidence bound is larger than a critical value.