Multidimensional model of opinion dynamics in social networks: polarization indices

We consider a multidimensional model of opinion dynamics in social networks. Within the framework of the model, the dynamics of two interconnected information processes in a social network is studied. The first process is the excitation of agents and their externally observed actions (e. g., in the form of messages published in the network). The second process, which has an obvious connection with the first one, is the formation of agents' opinions (which are a characteristic of their internal state). We demonstrate that the proposed model of opinion dynamics is flexible, allowing to take into account the significant effects of opinion formation in social networks, including consensus or agreement of opinions, preservation of differences in the agents' opinions, and even polarization of opinions. We propose approaches to measuring the polarization of opinions and present the simulation results. We show that the proposed polarization index for a network allows us to distinguish and evaluate situations with meaningfully different multidimensional distributions of opinions in a social network, as well as to find directions for the greatest polarization.