Representation of preferences á la Savage with a general probability measure

Abstract

This paper addresses two weaknesses of the subjective expected utility representation of Savage: The first is that the resulting subjective probability measure P is atomless only, the second is that P is only finitely additive. We give conditions under which a numerical representation of preferences is an expected utility á la Savage, but with respect to an arbitrary, countable additive probability measure. Savage has seven axioms in his theory, some of which are rather hard to interpret in an economic setting. One advantage with the theorem of this paper is that, essentially, one has to relate to only four axioms for the general representations to hold, all of which easy to interpret in economic terms.