 where \(u : \mathcal{X}\mapsto \mathbb{R}\) is a consequence utility function unique up to positive linear transformation and \(P: \mathcal{S}\mapsto [0,1]\) is a unique subjective probability function, satisfying \(P(\varnothing)=0\), \(P(\mathcal{S})=1\), and the finite additivity property \(P(A\cup B)=P(A)+P(B)\) for all disjoint events \(A,B\). In other words, \(U\) returns the sum of the utilities of the possible outcomes, each multiplied by the subjective probability of the set of states which are mapped onto that outcome.