Rédei, Miklós and Jing, Honglin
(2024)
Conditionally inaccessible decisions.
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Abstract
We define a notion of inaccessibility of a decision between two options represented by utility functions, where the decision is based on the order of the expected values of the two utility functions. The inaccessibility expresses that the decision cannot be obtained if the expectation values of the utility functions are calculated using the conditional probability defined by a prior and by partial evidence about the probability that determines the decision. Examples of inaccessible decisions are given in finite probability spaces. Open questions and conjectures about 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.
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