Consensus time in a concealed voter model with heterogeneous activity of voters

Abstract

We systematically study a concealed voter model with heterogeneous reaction rates including the copying rate, externalization rate and internalization rate of each voter, which corresponds to the heterogeneity of activity of real people. By means of heterogeneous mean-field treatment, we derive the evolution equations of the system which allow us to construct a conserved quantity that governs the dynamical process. And furthermore, we also obtain the analytical expressions for the consensus time along with the exit probability. Our studies suggest that the heterogeneous copying rate and internalization rate can decelerate the consensus process, whereas the heterogeneous externalization rate does the opposite but slightly. All the analytical predictions are validated by extensive computer simulations.