  Causal decision theory comes in many varieties, but I’ll consider a representative version proposed by Savage (1972), which calculates \(P_{A}(o)\) by summing the probabilities of states that, when combined with the act \(A\), lead to the outcome \(o\). Let \(f_{A,s}(o)\) be a of outcomes, which maps \(o\) to 1 if \(o\) results from performing \(A\) in state s, maps \(o\) to 0 otherwise. Then