Given the widespread integration of Social AI like ChatGPT, Gemini, Copilot, and MyAI, in personal and professional contexts, it is crucial to understand their effects on information and knowledge processing, and individual autonomy. This paper builds on Bråten’s concept of model power, applying it to Social AI to offer a new perspective on the interaction dynamics between humans and AI. By reviewing recent user studies, we examine whether and how models of the world reflected in Social AI may disproportionately impact human-AI interactions, potentially leading to model monopolies where Social AI impacts human beliefs, behaviour and homogenize the worldviews of its users. The concept of model power provides a framework for critically evaluating the impact and influence that Social AI has on communication and meaning-making, thereby informing the development of future systems to support more balanced and meaningful human-AI interactions.