Potential outcome and decision theoretic foundations for statistical causality

Abstract In a recent work published in this journal, Philip Dawid has described a graphical causal model based on decision diagrams. This article describes how single-world intervention graphs (SWIGs) relate to these diagrams. In this way, a correspondence is established between Dawid's approach and those based on potential outcomes such as Robins’ finest fully randomized causally interpreted structured tree graphs. In more detail, a reformulation of Dawid s theory is given that is essentially equivalent to his proposal and isomorphic to SWIGs.