CONDITIONALLY INACCESSIBLE DECISIONS

Abstract We define a notion of conditional inaccessibility of a decision between two actions represented by two utility functions defined in a finite probability space, where the decision is based on the order of the expected values of the two utility functions: a decision making Agent preferring the action with the higher expected utility. The conditional inaccessibility expresses that the decision cannot be obtained if the expectation values of the utility functions are calculated using the Jeffrey conditional probability defined by a prior and by partial evidence about the probability that determines the decision. Examples of conditionally inaccessible decisions are given, and it is shown that if a conditionally inaccessible decision exists in a probability space, then there exists a continuum number of conditionally inaccessible decisions in that probability space. Open questions and conjectures about the conditional inaccessibility of decisions are formulated. The results are interpreted as showing the crucial role of priors in Bayesian taming of epistemic uncertainties about probabilities that determine decisions based on utility maximizing.