I think this example is an interesting illustration of how difficult it is to “solve the academic coordination problem,” that is to be up to speed on what folks in related disciplines are up to.
Folks who actually worry about exposures like smoking (epidemiologists) are not only aware of this issue, they invented a special target of inference which addresses it. This target is called “effect of treatment on the treated,” (ETT) and in potential outcome notation you would write it like so:
E[C(s) | s] - E[C(s’) | s]
where C(s) is cancer rate under the smoking intervention, C(s’) is cancer rate under the non-smoking intervention, and in both cases we are also conditioning on whether the person is a natural smoker or not.
By the consistency axiom, E[C(s) | s] = E[C | s], but the second term is harder. In fact, the second term is very subtle to identify and sometimes may require untestable assumptions. Note that ETT is causal. EDT has no way of talking about this quantity. I believe I mentioned ETT at MIRI before, in another context.
In fact, not only have epidemiologists invented ETT, but they are usually more interested in ETT than the ACE (average causal effect, which is the more common effect you read about on wikipedia). In other words, an epidemiologist will not optimise utility with respect to p(Outcome(action)), but with respect to p(Outcome(action) | how you naturally act), precisely because how you naturally act gives information about how interventions affect outcomes.
The reason CDT fails on this example is because it is “leaving info on the table,” not because representing causal relationships is the wrong thing to do. The reason EDT succeeds on this example is because despite the fact that EDT is not representing the situation correctly, the numbers in the problem happen to be benign enough that the bias from not taking confounding into account properly is “cancelled out.”
The correct repair for CDT is to not leave info on the table. The correct repair for EDT, as always, is to represent confounding and thus become causal. This is also the lesson for Newcomb problems: CDT needs to properly represent the problem, and EDT needs to start representing confounding properly—it is trivial to modify Newcomb’s problem to have confounding which will cause EDT to give the wrong answer. That was the point of my FHI talk.
Thanks to Stuart for pointing me to this.
I think this example is an interesting illustration of how difficult it is to “solve the academic coordination problem,” that is to be up to speed on what folks in related disciplines are up to.
Folks who actually worry about exposures like smoking (epidemiologists) are not only aware of this issue, they invented a special target of inference which addresses it. This target is called “effect of treatment on the treated,” (ETT) and in potential outcome notation you would write it like so:
E[C(s) | s] - E[C(s’) | s]
where C(s) is cancer rate under the smoking intervention, C(s’) is cancer rate under the non-smoking intervention, and in both cases we are also conditioning on whether the person is a natural smoker or not.
By the consistency axiom, E[C(s) | s] = E[C | s], but the second term is harder. In fact, the second term is very subtle to identify and sometimes may require untestable assumptions. Note that ETT is causal. EDT has no way of talking about this quantity. I believe I mentioned ETT at MIRI before, in another context.
In fact, not only have epidemiologists invented ETT, but they are usually more interested in ETT than the ACE (average causal effect, which is the more common effect you read about on wikipedia). In other words, an epidemiologist will not optimise utility with respect to p(Outcome(action)), but with respect to p(Outcome(action) | how you naturally act), precisely because how you naturally act gives information about how interventions affect outcomes.
The reason CDT fails on this example is because it is “leaving info on the table,” not because representing causal relationships is the wrong thing to do. The reason EDT succeeds on this example is because despite the fact that EDT is not representing the situation correctly, the numbers in the problem happen to be benign enough that the bias from not taking confounding into account properly is “cancelled out.”
The correct repair for CDT is to not leave info on the table. The correct repair for EDT, as always, is to represent confounding and thus become causal. This is also the lesson for Newcomb problems: CDT needs to properly represent the problem, and EDT needs to start representing confounding properly—it is trivial to modify Newcomb’s problem to have confounding which will cause EDT to give the wrong answer. That was the point of my FHI talk.