Defier ($(D(0),D(1))=(1,0)$)

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,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.^[ref]