The main lesson for a student of causality is that a causal model entails more than merely drawing arrows. Behind the arrows, there are probabilities. When we draw an arrow from X to Y, we are implicitly saying that some probability rule or function specifies how Y would change if X were to change. We might know what the rule is; more likely, we will have to estimate it from data. One of the most intriguing features of the Causal Revolution, though, is that in many cases we can leave those mathematical details completely unspecified. Very often the structure of the diagram itself enables us to
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