If there is, I don’t know it.
There's a ton of work on general sensitivity analysis in the semi-parametric stats literature.
If there is really both reverse causation and regular causation between Xr and Y, you have a cycle, and you have to explain what the semantics of that cycle are (not a deal breaker, but not so simple to do. For example if you think the cycle really represents mutual causation over time, what you really should do is unroll your causal diagram so it's a DAG over time, and redo the problem there).You might be interested in this paper (https://arxiv.org/pdf/1611.09414.pdf) that splits the outcome rather than the treatment (although I don't really endorse that paper).
The real question is, why should Xc be unconfounded with Y? In an RCT you get lack of confounding by study design (but then we don't need to split the treatment at all). But this is not really realistic in general -- can you think of some practical examples where you would get lucky in this way?
"That’s the test. Would you put it in your arm rather than do nothing? And if the answer here is no, then, please, show your work."
Seems to be an odd position to take to shift the burden of proof onto the vaccine taker rather than than the scientist.
---I think a lot of people, you included, are way overconfident on how transmissible B.1.1.7. is.
90% of the work ought to go into figuring out what fairness measure you want and why. Not so easy. Also not really a "math problem." Most ML papers on fairness just solve math problems.
A whole paper, huh.
I am contesting the whole Extremely Online Lesswrong Way<tm> of engaging with the world whereby people post a lot and pontificate, rather than spending all day reading actual literature, or doing actual work.
"Unless you’d put someone vulnerable at risk, why are you letting another day of your life go by not living it to its fullest? "
As soon as you start advocating behavior changes based on associational evidence you leave the path of wisdom.
You sure seem to have a lot of opinions about statisticians being conservative about making claims without bothering to read up on the relevant history and why this conservativism might have developed in the field.
You can read Halpern's stuff if you want an axiomatization of something like the responses to the do-operator.
Or you can try to understand the relationship of do() and counterfactual random variables, and try to formulate causality as a missing data problem (whereby a full data distribution on counterfactuals and an observed data distribution on factuals are related via a coarsening process).