Defier (source code)
= Defier
{title2=$(D(0),D(1))=(1,0)$}
A defier is a unit with <potential treatment receipts> $D(0)=1$ and $D(1)=0$: it takes the <treatment> without encouragement but does not take it when encouraged. This is the $(1,0)$ <principal stratum>. The word specifies potential behavior under a particular binary intervention; it does not describe a general personality trait.
A <defier> contributes $-1$ to $D(1)-D(0)$, whereas a <complier> contributes $+1$. Consequently,
$$
\mathbb E[D(1)-D(0)]=\Pr(\text{complier})-\Pr(\text{defier}).
$$
The usual <instrumental-variable monotonicity> assumption sets the second probability to zero. A positive average effect of encouragement on receipt does not prove that there are no <defiers>: positive and negative individual changes can coexist.<Principal Stratification in Causal Inference by Constantine E. Frangakis and Donald B. Rubin>[Section 2, principal strata and treatment compliance]{ref}
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