Standard axiomatizations of expected-utility theory envision an agent with fixed probability assessments who can be observed to choose actions from varying opportunity sets (for instance, pairs of lotteries). These axiomatizations also envision that the agent's preferences among these actions depend on the state of nature only through the state-dependent consequences of the actions, and that these consequences are clearly defined and observable. The authors suggest that this conception may be an unnecessarily restrictive basis for empirical testing, and instead study the pattern of choices from a fixed set of actions as probability assessments change. They show that maximization of the expectation of a general, state-dependent utility function places nontrivial restrictions on such a choice pattern. These restrictions are completely characterized by a discrete version of an integrability condition.