Destabilizing a Social Network Model via Intrinsic Feedback Vulnerabilities

Social influence plays an important role in shaping individual opinions and actions, particularly in our digitally connected world. AI-generated, personalized content has led to serious and well-founded concerns, including United States Supreme Court Cases regarding the potential for the radicalization of individuals based on social influence. Motivated by these developments, we present a case study investigating the effects of small but intentional perturbations on the integrity of a simple social network. We employ Taylor's classic model of social influence and use tools from robust control theory (most notably the Dynamic Structure Function (DSF)), to identify precisely the perturbations that are sufficient to qualitatively alter the system's equilibrium and also minimal in norm. In particular, we examine two scenarios: perturbations to an existing link and perturbations taking the form of the addition of a new link to the network. In each case, we identify destabilizing perturbations and simulate their effects. Remarkably, we find that even small alterations to network structure may cause sentiments to grow in magnitude without bound, indicating the potential for large-scale shifts in collective behavior to be triggered by minor adjustments in social influence. Our findings emphasize the imperative need for further investigation into vulnerabilities in real-world social networks, where such dynamics may already exist.