Multidimensional Friedkin-Johnsen model with increasing stubbornness in social networks

Abstract

In most previous opinion dynamics research, the opinion evolution is usually defaulted to evolving over a single topic; however, in more general scenarios, agents often discuss several topics at the same time. This paper adopts a multidimensional opinion dynamics model in which the opinions are represented by vectors to reveal the multi-topic opinion pattern. To be more in line with reality, this paper employs a multidimensional version of the Friedkin-Johnsen (FJ) model, where each stubborn agent has a time-evolving stubbornness level. The theoretical analysis finds that the proposed model is convergent if the interpersonal influence matrix is stochastic indecomposable and aperiodic. To achieve unified consensus, opinion leaders are introduced, after which the consensus conditions for the proposed model are given. The theoretical conclusions suggest that in the proposed model, the stubborn agents are as prominent as the opinion leaders in the opinion formation process. Simulations are then conducted in two types of artificial networks, from which it is found that compared with the scalar version of the proposed model and standard multidimensional FJ models in which agents’ stubbornness levels remain unchanged, the proposed model produce a more compact final opinion space. The results show that to generate smaller opinion distance and higher opinion correctness degree, it is necessary to ensure a lower proportion of stubborn agents and higher network connectivity. This is consistent with people’s intuition. The population size is found to have little effect on the results, but larger number of topics result in larger opinion distances. These findings are enlightening and helpful to opinion managers.