Model of opinion dynamics caused by information pressure in multi-agent system with stochastic activation of links

Abstract

The dynamic properties of a modified nonlinear noisy voter model on a square lattice are studied in the paper. The introduced modifications are as follows. First, the changes of the binary variable (opinion) at the voters (agents) are caused by avalanche-like perturbations of the system. Secondly, the structure of inter-agent links is not static. Its temporal evolution is due to a new characteristic of the agent called ‘activity’. It determines the probability for the agent to be linked with its nearest neighbors at a given time moment. In addition we introduce a binary variable that changes randomly in time (an ‘external opinion’). According to the proposed rules for opinion changes, an agent that unlinked to neighbors changes its opinion to a current value of the external opinion, regardless of the opinions of other agents. A linked agent can copy the opinion of its neighbor during an avalanche process. Analytically and numerically, we show that the agents’ ‘activity’ distribution and the time-averaged value of the external opinion completely determines the mode of opinion dynamics. The phase diagram for the model under consideration is obtained. In the case of large values of averaged agents’ ‘activity’ the system switches between two consensus states spending the most of time in the consensus with shared opinion corresponding to the prevailing value of the external opinion. For small value of averaged ‘activity’ the system tends to the state where the opposite opinions coexist, but agents predominate with opinion corresponding to sign of the time-averaged value of the external opinion. We demonstrate that the resulting model reflects the main features of the behavior of real multi-agent systems where the external information inflows into the system and, spreading among agents, drives opinion dynamics.