Contrary to common belief, Savage's axioms do not imply strict stochastic dominance. Instead, they usually involve violation of that. Violations occur as soon as the range of the utility function is rich enough, e.g. contains an interval, and the probability measure is, loosely speaking, "constructive". An example is given where all of Savage's axioms are satisfied, but still strict statewise monotonicity is violated: An agent is willing to exchange an act for another act that with certainty yields a strictly worse outcome. Thus book can be made against the agent. Weak stochastic dominance and weak statewise monotonicity are always satisfied, as well as strict stochastic dominance and strict statewise monotonicity when restricted to acts with finitely many outcomes.

Savage's axioms, stochastic dominance
The Review of Economic Studies
Erasmus School of Economics

Wakker, P.P. (1993). Savage's Axioms Usually Imply Violation of Strict Stochastic Dominance. The Review of Economic Studies, 60(2), 487–493. Retrieved from