Potential Outcome and Decision Theoretic Foundations for Statistical Causality

TL;DR

This paper explores the theoretical connections between Dawid's decision diagram approach and potential outcomes frameworks, establishing a formal correspondence and reformulation to unify different causal inference models.

Contribution

It provides a reformulation of Dawid's causal theory that aligns with SWIGs and potential outcomes, bridging different causal modeling approaches.

Findings

Established a formal correspondence between Dawid's diagrams and SWIGs

Reformulated Dawid's theory to be equivalent and isomorphic to SWIGs

Unified decision-theoretic and potential outcome frameworks in causal inference

Abstract

In a recent paper published in the Journal of Causal Inference, 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.