= Solution
Let $Y(1)$ and $Y(0)$ be the <potential outcomes> for the same individual under well-defined interventions setting the binary <exposure> to 1 and 0. The <average treatment effect>, also called the average <causal effect> on the additive scale, is
$$
\boxed{\operatorname{ACE}=\mathbb E[Y(1)-Y(0)]=\mathbb E[Y(1)]-\mathbb E[Y(0)].}
$$
The average is over the target population. This compares hypothetical outcomes under two interventions, rather than the observed difference $\mathbb E[Y\mid X=1]-\mathbb E[Y\mid X=0]$, which can be distorted by <confounding>. For binary $Y$, the displayed contrast is a causal risk difference. <Consistency in causal inference> and a well-defined intervention, including an appropriate no-<interference in causal inference> assumption, give these <potential outcomes> their meaning.
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