If a decision maker, in a world of uncertainty à la Anscombe and Aumann (1963), can choose acts according to some objective probability distribution (by throwing dice for instance) from any given set of acts, then there is no set of acts that allows an experimenter to test more than the Axiom...

A decision maker (DM) is asked to make choices from a set of acts, which entail both risk and uncertainty in the sense of knight (1921). Extending Raiffa's (1961) argument I show that, provided the DM can choose acts objectively randomly (by flipping her own fair coin, for instance), provided...