Subjective Probabilities on Subjectively Unambiguous Events

The paper suggests a behavioural definition of (subjective) ambiguity in an abstract setting where objects of choice are Savage-style acts. Then axioms are described that deliver probabilistic sophistication of preference on the set of unambiguous acts. In particular, both the domain and the values of the decision-maker's probability measure are dervied from perference, delivering thereby a 'fully subjective' theory of probability. It is argued that the noted result also provides a decision-theoretic foundation for the Knightian distinction between risk and ambiguity and that it provides a unifed framework for analysing attitudes towards risk and towards ambiguity.