Abstract
This is a study of probabilistically sophisticated choice behavior when the preference relation is incomplete. Invoking the analytical framework of Anscombe and Aumann (1963) and building on the work of Machina and Schmeidler (1995), the paper provides an axiomatic characterization of the general multi-prior multi-utility probabilistically sophisticated representation. In addition, the paper examines the axiomatic foundations for two special cases: complete beliefs and complete tastes. In the former case, the incompleteness is due to ambiguous tastes and in latter case it is due to ambiguous beliefs.
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