One school of statistical thought holds that statistical decisions, when "rationally" made, are (and must be) made as if there were an a priori distribution on the states of Nature. Here "rational" means according to some set of axioms of "rational" choice of a decision function. In the present paper one aspect of one such axiom system is examined. The system is one of the simplest which has been proposed and can be regarded as a prototype of the others. It is argued that one of its axioms does not, upon closer scrutiny, appear very plausible and reasonable. It is demonstrated that this axiom requires the experimenter to have a preference among the states of Nature in advance of the experiment. Some related questions are discussed.