= Complier
{title2=$(D(0),D(1))=(0,1)$}
A complier is a unit with <potential treatment receipts> $D(0)=0$ and $D(1)=1$: binary encouragement $Z$ changes its receipt from no <treatment> to <treatment>. This $(0,1)$ pair defines a <principal stratum>, rather than a behavior inferred from one observed assignment.
For example, a unit that participates exactly when invited is a <complier>. Under <instrumental-variable monotonicity>, which excludes <defiers>,
$$
\mathbb E[D(1)-D(0)]=\Pr(\text{complier}).
$$
Thus, with randomized assignment, the difference in treatment-receipt rates estimates the complier fraction. To interpret an outcome-rate ratio as the <local average treatment effect>, one additionally needs the relevant independence and exclusion assumptions and a nonzero complier fraction. An observed encouraged participant may instead be an <always-taker>.<Principal Stratification in Causal Inference by Constantine E. Frangakis and Donald B. Rubin>[Section 2, cross-classification by intermediate potential values]{ref}
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