States, models and information: A reconsideration of Ellsberg's paradox

Abstract

We show that a general process of decision making involves uncertainty about two different sets: the domain of the acts and another set, which we call the set of models for the decision maker. We study the effect of different information structures on the set of models, and prove the existence of a dichotomy: either the decision maker's ranking of the acts obeys Subjective Expected Utility theory or there are many events to which probabilities cannot be assigned. We use this result to formalize the idea of Knightian Uncertainty. The relevance of information structures associated to Knightian Uncertainty is shown by means of examples, one of which is a version of Ellsberg's experiments. Our findings show that a decision maker faces, generally speaking, uncertainties of two different types - "uncertainty about which state obtains" and "uncertainty about how the world works" and that Savage's theory considers only uncertainty of the first type. Finally, in situations of Knightian Uncertainty, we identify the class of events to which probabilities can be assigned, and study the relation with the class of unambiguous events in the sense of [13] and [25].

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