Opinion dynamics in modified expressed and private model with bounded confidence

Abstract

In a social network, an individual may express an opinion against his/her own private opinion. Moreover, during the evolution of opinion dynamics, an individual may only accept parts of opinions that are similar to his/her own opinion. These phenomenons bring new challenges to the study of the opinion dynamics. In this paper, we propose a modified expressed-private-opinion (MEPO) model with bounded confidence. In the MEPO model, two categories of neighborhood relationships, namely, the communication neighbor and the opinion neighbor, are proposed. More specifically, the communication neighbor represents the information flow among individuals while the opinion neighbor, which is a subset of the communication neighbor, implies whether or not the corresponding opinions will be accepted to be incorporated into the individual’s opinion updating process. Furthermore, the scope of the opinion neighbor is determined by the confidence level such that the whole group is divided into open-minded, moderate-minded, and closed-minded individuals accordingly. As a result, an individual’s private opinion in the proposed MEPO model evolves by his/her own private opinion and the stubbornness value, and also the impacts from the expressed opinions of the opinion neighbors.Specifically, we focus on the design of the stubbornness parameter λ, i.e., one’s stubbornness to his/her initial private opinion. By different scenarios, three expression formats are taken into consideration including (1) λ with constant value 1; (2) λ monotonously increasing to 1; and (3) λ determined by the rate of opinion neighbor number over communication neighbor number. A series of experiments are designed to analyze the relation between the stubbornness parameter λ and the final opinion cluster number. The experimental results show that the final cluster number is mainly determined by both of the rate of closed-minded individuals and λ: it is inversely proportional to the rate of closed-minded individuals as well as the growth rate of λ.