L. J. 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...

F. J. Anscombe and R. J. Aumann (1963) showed that, if one accepts the existence of a physical randomizing device such as a roulette wheel, then L. J. Savage's derivation of subjective expected utility can be considerably simplified. They, however, invoked compound gambles to define their...