A norm of 50–50 division appears to have considerable force in a wide range of economic environments, both in the real world and in the laboratory. Even in settings where one party unilaterally determines the allocation of a prize (the dictator game), many subjects voluntarily cede exactly half to another individual. The hypothesis that people care about fairness does not by itself account for key experimental patterns. We consider an alternative explanation, which adds the hypothesis that people like to be perceived as fair. The properties of equilibria for the resulting signaling game correspond closely to laboratory observations. The theory has additional testable implications, the validity of which we confirm through new experiments.