## Counterfactual quantities

Using structural model semantics, Pearl gives definitions of six counterfactual quantities.

Let be a random variable representing a binary outcome after a binary treatment is forced to value ; and let and denote events and , and their complements.

Probability that the absence of event would prevent event , given that in fact and did occur. — attribution

Probability that the presence of event would produce event , given that in fact and did not occur. — susceptibility

Probability that the absence of event would prevent event and the presence of event would produce event . — necessary and sufficient cause

Probability that the absence of event would prevent event , given that in fact did occur. — proportion of observed cases in the total population that would not have occurred had the population been entirely unexposed (disablement)

Probability that the presence of event would produce event , given that in fact did not occur. — enablement

Probability that the presence of event would produce event , given that in fact did not occur. — Effect of treatment on the treated