Code of simulation experiments.

The dynamics of social influence carry significant sociological and economic implications and have been examined across various disciplines. However, the dynamics of social influence within tag-mediated systems remains underexplored. This study proposes a generalized networked urn model that incorporates tagging effects, extending current understandings of self-reinforcing and self-correcting mechanisms in social dynamics. Mathematical derivations show that tag-related parameters—the share of individuals with a given tag, the probability of being tag-driven, and the effect of tag difference—interact with social influence to shape convergence outcomes. Depending on context, tags can either reinforce early advantages or act as a corrective force that drives outcomes toward balance. Simulation results further indicate that tagging effects may weaken path dependence under certain conditions, reducing market inequality and improving predictability, while in other cases they may sustain disparities. These findings underscore the moderating role of tags in collective dynamics, offering theoretical insights into the social influence processes.