Provability Counterfactuals vs Three Axioms of Galles and Pearl 2015-08-30T02:48:13.000Z

Comment by IAFF-User-52 (Imported-IAFF-User-52) on Causal graphs and counterfactuals · 2016-09-01T23:46:44.000Z · LW · GW

The problem is indeed that $P\left(B|A\right)$ is insufficient to compute a unique counterfactual---additional causal information is needed. Pearl's approach is to specify each observable variable as a deterministic function of its parents in the causal graph. Any uncertainty must be represented by a set of "exogenous" variables $U$, which can feature in the functions for the observables. (See chapter 7 of Causality, or also An Axiomatic Characterization of Causal Counterfactuals.)

For example, your first process could be represented by the following causal model:

$A\left(X\right)=XB(A,Y)=\neg (A\oplus Y)P\left(X\right)=pP\left(Y\right)=0.75$

The other processes might have different structures, equations, and distributions $P(X,Y)$---it's not possible in general to distinguish these purely from the distribution $P(A,B)$.