Conditional exchangeability

In a binary-treatment potential outcomes model, conditional exchangeability given pretreatment covariates $X$ is $(Y(0),Y(1))\perp A\mid X$. Within each covariate stratum, treatment assignment then carries no information about the relevant potential outcomes. Together with consistency in causal inference and positivity, it permits outcome standardization to identify average causal contrasts. The assumption concerns unobserved counterfactual outcomes and cannot be established just by checking balance of the measured covariates. Including a large list of predictors is not by itself a guarantee that the assumption holds.