Evolutionary dynamics of the weighted voter model with opinion strength on complex networks

The voter model has served to address the emergence of consensus within populations of individuals. However, the dynamics based on the classic voter model has usually been analyzed based on the assumption that the two states in the model are simply equivalent. In this paper, we discuss a mathematical description of the weighted voter model and obtain a series of results for the evolutionary process on complex networks. For homogeneous networks, we study the active link density analytically and find that the opinion strength plays a crucial role in determining whether the system can reach consensus. We also extend our research to heterogeneous networks and discover that the network structure can affect the convergence time but has less influence on the positive proportion. The results can be applied to various pervasive cases in which two conflicting opinions interact with each other.