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Complexity of the problem of choosing among uncertain acts is a salient feature of many of the environments in which departures from expected utility theory are observed. I study a class of Generalized Simple Bounds preferences in which acts that are complex from the perspective of the decision maker are bracketed by "simple" acts to which they are related by statewise dominance. I then study a refinement of the model in which the size of the partition with respect to which an act is measurable arises endogenously as a measure of subjective complexity. Finally, I consider choice behavior characterized by a "cautious completion" of Simple Bounds preferences, and discuss the relationship between this model and models of ambiguity aversion. I develop general comparative statics results, and explore applications to portfolio choice and insurance choice. • Problems of choice problems under uncertainty are complex. • From behavioral axioms, I characterize the set of acts that are well-understood. • Decision makers use acts they understand well to bracket those they do not. • The model is tractable, and admits rich comparative statics. • The model helps explain observed choice patterns in applications. [ABSTRACT FROM AUTHOR]

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage's postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework. [ABSTRACT FROM AUTHOR]