A nudge is a non-coercive paternalistic intervention that attempts to improve choices by manipulating the framing of a decision problem. As any paternalism, it faces the difficulty of determining the appropriate welfare criterion. We propose a welfare-theoretic foundation for nudging similar in spirit to the classic revealed preference approach, by investigating a model where preferences and mistakes of an agent have to be elicited from her choices under different frames. We provide characterizations of the classes of behavioral models for which nudging is possible or impossible. For the case where nudging is possible in principle, we derive results on the required quantity of information.