Social robots must take on many roles when interacting with people in everyday settings, some of which may be authoritative, such as a nurse, teacher, or guard. It is important to investigate whether and how authoritative robots can influence people in applications ranging from health care and education to security and in the home. Here, we present a human-robot interaction study that directly investigates the effect of a robot's peer or authority role (formal authority) and control of monetary rewards and penalties (real authority) on its persuasive influence. The study consisted of a social robot attempting to persuade people to change their answers to the robot's suggestion in a series of challenging attention and memory tasks. Our results show that the robot in a peer role was more persuasive than when in an authority role, contrary to expectations from human-human interactions. The robot was also more persuasive when it offered rewards over penalties, suggesting that participants perceived the robot's suggestions as a less risky option than their own estimates, in line with prospect theory. In general, the results show an aversion to the persuasive influence of authoritative robots, potentially due to the robot's legitimacy as an authority figure, its behavior being perceived as dominant, or participant feelings of threatened autonomy. This paper explores the importance of persuasion for robots in different social roles while providing critical insight into the perception of robots in these roles, people's behavior around these robots, and the development of human-robot relationships.