Co-Evolution of Dual Opinions Under Asynchronous Updating

Inspired by the dual attitudes theory that implicit opinions are individuals' inner evaluations affected by experience while explicit opinions are external expressions of these evaluations, we propose an asynchronous co-evolution model of dual opinions, where individuals update explicit opinion at each time step but change their implicit opinion based on their own clock. Furthermore, we introduce the after-effect of observed opinion information in this model, which enables individuals to update implicit opinions not only based on the opinion information observed at the current time but also on the information received from the past period of time. We analyze the dynamics of dual opinions in two discussion scenarios: a group of individuals with similar and opposite initial opinions. In the former scenario, rigorous analysis suggests that dual opinions are polarized to extreme opinions, mathematically verifying the empirical finding that group discussion intensifies individuals' preferences, resulting in group polarization. In the latter scenario, our investigation shows that individuals with low bias show acceptance (inward conformity) while those with high bias exhibit compliance (outward conformity). We further analyze the influence of parameters on the co-evolution of dual opinions.