Nontransitive measurable utility for decision under uncertainty.

We axiomatize a representation for preference between acts in Savage's formulation for decision under uncertainty that is based on expectation of a nonseparable utility function on pairs of consequences with respect to the decision maker's subjective probability measure over states. The representation has been discussed previously by Graham Loomes and Robert Sugden, David Bell, and the present author. The representation follows from Savage's axioms for subjective expected utility when his ordering axiom is weakening and his conditional dominance principle is added as an explicit axiom. All axioms except the Arhemedean condition are necessary for the nonseparable representation.