‘Expected utility / subjective probability’ analysis without the sure-thing principle or probabilistic sophistication

Summary.The basic analytical concepts, tools and results of the classical expected utility/subjective probability model of risk preferences and beliefs under subjective uncertainty can be extended to general “event-smooth” preferences over subjective acts that do not necessarily satisfy either of the key behavioral assumptions of the classical model, namely the Sure-Thing Principle or the Hypothesis of Probabilistic Sophistication. This is accomplished by a technique analogous to that used by Machina (1982) and others to generalize expected utility analysis under objective uncertainty, combined with an event-theoretic approach to the classical model and the use of a special class of subjective events, acts and mixtures that exhibit “almost-objective” like properties. The classical expected utility/subjective probability characterizations of outcome monotonicity, outcome derivatives, probabilistic sophistication, comparative and relative subjective likelihood, and comparative risk aversion are all globally “robustified” to general event-smooth preferences over subjective acts.

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