Preliminary and obviously incomplete A CONSEQUENTIALIST APPROACH TO AMBIGUITY

An outcome is ambiguous if it is an incomplete description of the probability distribution over consequences. An incomplete description is identified with the set of probabilities that satisfy the incomplete description. A choice problem is ambiguous if the decision maker is choosing between incompletely described outcomes, that is, between sets of probabilities. This paper develops the theory of ambiguous choice problems as a continuous, linear extension of expected utility preferences from probabilities to sets of probabilities. Roughly, risk refers to situations where the likelihood of relevant events can be represented by a probability measure, while ambiguity refers to situations where there is insufficient information available for the decision maker to assign probabilities to events. (Epstein and Zhang [7])