Consider we want to compare I{I1,I2,I3...In} (a set of manipulable interventions) on outcome Y.  I didn't affect Y directly but through X.  See casual diagram below.

I->X->Y

For example, I are different diets, Y is life expectancy.  X is lowering cholesterol levels. 

The ideal intervention will be I has no effect on Y but affect  X deterministically, its resultant effect on Y will be Q. However, this is ideal which is not feasible right now. So Q can be considered a "theoretical limit"
 

University of Michigan - Ann Arbor


Assuming an observational study guided by model M, we identify and evaluate the Q with the expression Q = E[Y |do(x)] = q(x), where q(x) is a function of x computed from the joint distribution of observed variables in the model. 

One can use this information in three ways:
1. Q represents a limit on pending interventions
2. Q tells us about the effects of feasible interventions
3. Q serves as an auxiliary mathematical operation in the derivation of causal effects of manipulable variables.


The Semantics of Q 

Pearl, Judea. “On the Interpretation of Do(x).” Technical Report - UCLA, 13 Feb. 2019.

https://ftp.cs.ucla.edu/pub/stat_ser/r486.pdf


On the Interpretation of do(x)

Example of Q as a limit on pending interventions

Q  has it's benefits to policymakers 
Consider a casual diagram I → X → Y, there is no link from I to Y

The overall effect of I on Y can be written in this formula.
E(Y |do(I)) = sum（P(x|do(I))E[Y |do(x)]）
SO if X->Y is 0 ,then I->Y is zero.

For example, 
X is smoking, y is cancer, I is increasing cigarette taxes. “if careful scientific investigations reveal that smoking has no effect on cancer, we can comfortably conclude that increasing cigarette taxes will not decrease cancer rates and that it is futile for schools to invest resources in anti-smoking educational programs.

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