Dynamic opinion updating with endogenous networks

Polarization is a well-documented phenomenon across a wide range of social issues. However, existing theories often treat the evolution of individual opinions and the formation of social networks as separate processes. In this study, we examine how individuals dynamically adjust their opinions while simultaneously forming and dissolving social connections, highlighting the interconnected nature of these behaviors. Our model is based on two key parameters: the direct benefit individuals receive from social connections and their willingness to adapt their opinions to align with their social circle. We identify conditions under which the network fails to achieve full connectivity, leading to persistent polarization of opinions. Additionally, our model demonstrates that polarization can temporarily increase during the transition to consensus, depending on the initial distribution of opinions and network structure. We explore the connection between these scenarios and a critical network metric: the initial diameter, under specific conditions related to the initial distribution of opinions.