Before revision: Savage proved that, if the decision-maker adheres to axioms of rationality, believing an uncertain event has possible outcomes each with a utility of then the person's choices can be explained as arising from this utility function combined with the subjective belief that there is a probability of each outcome, The subjective expected utility is the resulting expected value of the utility, If instead of choosing the person were to choose the person's subjective expected utility would be Which decision the person prefers depends on which subjective expected utility is higher.
After revision: Savage proved that, if the decision-maker adheres to axioms of rationality, baelieving an uncertain event has possible outcomes each with a utility of then the person's choices can be explained as arising from this utility function combined with the subjective belief that there is a probability of each outcome, The subjective expected utility is the resulting expected value of the utility, If instead of choosing the person were to choose the person's subjective expected utility would be Which decision the person prefers depends on which subjective expected utility is higher.