This paper proposes a formulation of consumer sovereignty, for use in normative economics, which does not presuppose individuals' preferences to be coherent. The fundamental intuition, that opportunity and responsibility have moral value, is formalised as a responsibility criterion for assessing opportunities in an economic system. A model of an exchange economy is presented, in which rational arbitrageurs compete to make profits by trading with non-rational consumers. In equilibrium, this economy satisfies the responsibility criterion. One interpretation of this result is that, in a competitive environment, the overall effects of money pumps are benign, even if individuals' preferences are persistently incoherent.