2/ deals with side effects in experimental settings). In this sense one can safely say that SCM provides legitimization for the logic of PO, but rejects PO as a "framework" or "approach" #Bookofwhy
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1/ Another important clarification. In what way does SCM embrace the logic of PO? Ans. It supports the consistency rule Y_x = Y if X=x, which is the main inference engine of PO. Consistency a theorem in SCM https://ucla.in/2MlB5Utand and an assumption in PO (part of SUTVA, whichhttps://twitter.com/yudapearl/status/1223161698875367424 …
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@yudapearl: as an example:if the intervention was a specific surgery, which could be practically performed differently by different surgeons, would you argue that this does not violate the consistency assumption/theorem because this should have been already encoded in the SCM? -
One argument is, indeed, that it should have been encoded in the SCM. Another, that it should be treated as "disjuctive action", and extrapolated by imaging: https://ftp.cs.ucla.edu/pub/stat_ser/r359-reprint-forthcoming.pdf …
#Bookofwhy
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If consistency is a theorem in SCM and an assumption in PO, does that not just mean that assumptions which were strong enough to imply consistency for any intervention on any graph were included in the axioms for your SCM model?
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In other words: at the point where user makes a causal model for a specific setting, the PO model allows them to either assume consistency or not depending on beliefs about reality, whereas SCM makes the decision for them: the consistency assumptions were just moved to the axioms
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I think the link should be http://ucla.in/2MlB5Ut ?
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2/ And, as a consequence, an analysis which does not distinguish the different versions of treatment is thus rather in disagreement with the SCM itself than with the consistency theorem?
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