A simple axiomatization of risk-averse expected utility

An agent's preferences exhibit risk aversion with respect to some probabilities of states of the world if she prefers deterministic outcome equal to the expected value of a state-contingent outcome under these probabilities to the state-contingent outcome itself. We show that if preferences exhibit risk aversion with respect to some probabilities and satisfy the independence axiom (sure thing principle), then they have an expected utility representation with respect to these probabilities. Since the independence axiom is necessary and sufficient for state-separable utility representation [Debreu, G., 1959. Topological methods in cardinal utility theory. In: Arrow, K., Karlin, S., Suppes, P. (Eds.), Mathematical Methods in Social Sciences. Standford University Press], our result shows that, given separable utility representation, expected utility follows from risk aversion.