Subjectively Expected State-Independent Utility on State-Dependent Consequence Domains

The standard decision theories of Savage and of Anscombe and Aumann both postulate that the domain of consequences is state independent. But this hypothesis makes no sense when, for instance, there is a risk of death or serious injury. The paper considers one possible way of deriving subjective probabilities and utilities in this case also. Moreover, the utilities will be state independent in the sense of giving equal value to any consequence that happens to occur in more than one state dependent consequence domain. The key is to consider decision trees having "hypothetical" probabilities attached to states of nature, and even to allow hypothetical choices of these probabilities.