Expected utility in decision-making situations with random in a broad sense consequences
Abstract
An extension of the expected utility theorem for decision-making situations with random in a broad sense consequences is proposed. The statistical regularity of a corresponding random phenomenon is a family of finitely additive probability measures. This family has an objective origin and taken as a whole describes the regularity of a random phenomenon. Statistical regularities on the set of consequences correspond to decisions. Natural conditions on a preference relation on the set of all statistical regularities are proposed. It is shown, that they are necessary and sufficient for the existence and uniqueness of the utility functional that is a minimum of the expected utility of the elements of a statistical regularity. The result is applied to solving decision-making problems, measuring the information content of an xperiment and the uncertainty of a decision-making situation.References
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