 \(\mathbf{U}(X)\) in turn is defined as the probability-weighted average of the utility \(u\) of all the possible worlds \(w\) in which \(X\) is true. For unconditional preferences the weighing is built on the probability function \(P\) that represents the agent’s actual information. The conditional preference ordering \(\succcurlyeq_A\), in contrast, is based on \(P_A\), the probability distribution representing the counterfactual scenario that the agent accepts proposition \(A\) as true. (For more discussion on the existence and uniqueness conditions of conditional preferences, see Luce and Krantz 1971, Joyce 1999, chapter 4, Bradley 1999). Jeffrey shows that the posterior utility function \(\mathbf{U}_A\) is related to the prior utility function \(\mathbf{U}\) as follows: