Notes on self-confidence in opinion dynamics

In some research involving opinion formation, there are some details that have not been studied deeply, just as the role of a person's self-confidence in opinion dynamics. This small but important detail needs to be cleared up. Hence, in this paper, we want to discuss the self-confidence in opinion dynamics with regard to some common linear and nonlinear models: DeGroot, Friedkin-Johnsen, Deffuant-Weisbuch and Hegselmann-Krause (HK) model. We unfold that (1) A person's self-confidence assumption has an important impact on the consensus condition in DeGroot model; (2) The relationship between the self-confidence on the initial opinion and the current opinion follows a Kuznets curve in Friedkin-Johnsen model; (3) A person's self-confidence has a close relationship with the convergence parameter in Deffuant-Weisbuch model, which has little impact on the number of opinion clusters at the stable stage; and (4) A person's self-confidence varies with time at first and then stays at a certain level finally in the HK model, while the person's self-confidence does not change with time in above three models.