Political opinion formation: Initial opinion distribution and individual heterogeneity of tolerance

Opinion dynamics on networks have received serious attention for its profound prospects in social behaviours and self-organized systems. However, political opinion formation, as one typical and significant case, remains lacking in discussion. Previous agent-based simulations propose various models that are based on different mechanisms like the coevolution between network topology and status transition. Nonetheless, even under the same network topology and with the same simple mechanism, forming opinions can still be uncertain. In this work, we propose two features, the initial distribution of opinions and the individual heterogeneity of tolerances on opinion changing, in political opinion formation. These two features are imbedded in the network construction phase of a classical model. By comparing multi simple-party systems, along with a detailed analysis on the two-party system, we capture the critical phenomenon of fragmentation, polarization and consensus both in the persistent stable stage and in-process. We further introduce the average ratio of nearest neighbours to characterize the stage of opinion formation. The results show that the initial distribution of opinions leads to different evolution results on similar random networks. In addition, the existence of stubborn nodes plays a special role: only nodes that are extremely stubborn can cause the change of final opinion distribution while in other cases they only delay the time to reach stability. If stubborn nodes are small in number, their effects are confined within a small range. This theoretical work goes deeper on an existing model, it is an early exploration on qualitative and quantitative simulation of party competition.