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A wide range of studies in Human-Robot Interaction (HRI) has shown that robots can influence the social behavior of humans. This phenomenon is commonly explained by the Media Equation. Fundamental to this theory is the idea that when faced with technology (like robots), people perceive it as a social agent with thoughts and intentions similar to those of humans. This perception guides the interaction with the technology and its predicted impact. However, HRI studies have also reported examples in which the Media Equation has been violated, that is when people treat the influence of robots differently from the influence of humans. To address this gap, we propose a model of Robot Social Influence (RoSI) with two contributing factors. The first factor is a robot’s violation of a person’s expectations, whether the robot exceeds expectations or fails to meet expectations. The second factor is a person’s social belonging with the robot, whether the person belongs to the same group as the robot or a different group. These factors are primary predictors of robots’ social influence and commonly mediate the influence of other factors. We review HRI literature and show how RoSI can explain robots’ social influence in concrete HRI scenarios.