Decision making, symmetry and structure: Justifying causal interventions

We can use structural causal models (SCMs) to help us evaluate the consequences of actions given data. SCMs identify actions with structural interventions. A careful decision maker may wonder whether this identification is justified. We seek such a justification. We begin with decision models, which map actions to distributions over outcomes but avoid additional causal assumptions. We then examine assumptions that could justify causal interventions, with a focus on symmetry. First, we introduce conditionally independent and identical responses (CIIR), a generalisation of the IID assumption to decision models. CIIR justifies identifying actions with interventions, but is often an implausible assumption. We consider an alternative: precedent is the assumption that “what I can do has been done before, and its consequences observed,” and is generally more plausible than CIIR. We show that precedent together with independence of causal mechanisms (ICM) and an observed conditional independence can justify identifying actions with causal interventions. ICM has been proposed as an alternative foundation for causal modelling, but this work suggests that it may in fact justify the interventional interpretation of causal models.