Expected utility theory from the frequentist perspective

We present an axiomatization of expected utility from the frequentist perspective. It starts with a preference relation on the set of infinite sequences with limit relative frequencies. We consider three axioms parallel to the ones for the von Neumann-Morgenstern (vN-M) expected utility theory. Limit relative frequencies correspond to probability values in lotteries in the vN-M theory. This correspondence is used to show that each of our axioms is equivalent to the corresponding vN-M axiom in the sense that the former is an exact translation of the latter. As a result, a representation theorem is established: The preference relation is represented by an average of utilities with weights given by the relative frequencies.