 where \(W_j\) is a world and \(P^A\) stands for the probability image of \(A\). Weirich (2001: Secs. 3.2, 4.2.2), as Sobel does, substitutes \(U(A \mbox{ given }S_i)\) for \(U(A \amp S_i)\) in the formula for expected utility and interprets \(U(A \mbox{ given }S_i)\) as the utility of the outcome that \(A\)’s realization would produce if \(S\) obtains. Accordingly, \(U(A \mbox{ given }S_i)\) responds to \(A\)’s causal consequences in worlds where \(S_i\) holds. Then the formula