Then, H is considered to be a precursor of G in universe Θ when there is some H-policy σ s.t. applying the counterfactual ”H follows σ” to Θ (in the usual infra-Bayesian sense) causes G not to exist (i.e. its source code doesn’t run).
A possible complication is, what if Θ implies that H creates G / doesn’t interfere with the creation of G? In this case H might conceptually be a precursor, but the definition would not detect it.
Can you please explain how does this not match the definition? I don’t yet understand all the math, but intuitively, if H creates G / doesn’t interfere with the creation of G, then if H instead followed policy “do not create G/ do interfere with the creation of G”, then G’s code wouldn’t run?
Can you please give an example of a precursor that does match the definition?
The problem is that if Θ implies that H creates G but you consider a counterfactual in which H doesn’t create G then you get an inconsistent hypothesis i.e. a HUC which contains only 0. It is not clear what to do with that. In other words, the usual way of defining counterfactuals in IB (I tentatively named it “hard counterfactuals”) only makes sense when the condition you’re counterfactualizing on is something you have Knightian uncertainty about (which seems safe to assume if this condition is about your own future action but not safe to assume in general). In a child post I suggested solving this by defining “soft counterfactuals” where you consider coarsenings of Θ in addition to Θ itself.
Can you please explain how does this not match the definition? I don’t yet understand all the math, but intuitively, if H creates G / doesn’t interfere with the creation of G, then if H instead followed policy “do not create G/ do interfere with the creation of G”, then G’s code wouldn’t run?
Can you please give an example of a precursor that does match the definition?
The problem is that if Θ implies that H creates G but you consider a counterfactual in which H doesn’t create G then you get an inconsistent hypothesis i.e. a HUC which contains only 0. It is not clear what to do with that. In other words, the usual way of defining counterfactuals in IB (I tentatively named it “hard counterfactuals”) only makes sense when the condition you’re counterfactualizing on is something you have Knightian uncertainty about (which seems safe to assume if this condition is about your own future action but not safe to assume in general). In a child post I suggested solving this by defining “soft counterfactuals” where you consider coarsenings of Θ in addition to Θ itself.
Thank you.