And in such cases, it is perfectly possible to remove the correlation in the same way that you say. If I know how Omega is deciding who is likely to one-box and who is likely to two-box, I can purposely do the opposite of what he expects me to do.
Exactly; but since a vast majority of players won't do this, Omega can still be right most of the time.
But if you want to solve the real problem, you have to solve it in the case of 100% correlation, both in the original Newcomb's problem and in this case.
Can you formulate that scenario, then, or point me to somewhere it's been formulated? It would have to be a world with very different cognition than ours, if genes can determine choice 100% of the time; arguably, genes in that world would correspond to brain states in our world in a predictive sense, in which case this collapses to regular Newcomb, and I'd one-box.
The problem presented by the gene-scenario, as stated by OP, is
Now, how does this problem differ from the smoking lesion or Yudkowsky's (2010, p.67) chewing gum problem?
However, as soon as you add in a 100% correlation, it becomes very different, because you have no possibility of certain outcomes. If the smoking lesion problem was also 100%, then I'd agree that you shouldn't smoke, because whatever "gene" we're talking about can be completely identified (in a sense) with my brain state that leads to my decision.
You are right that 100% correlation requires an unrealistic situation. This is true also in the original Newcomb, i.e. we don't actually expect anything in the real world to be able to predict our actions with 100% accuracy. Still, we can imagine a situation where Omega would predict our actions with a good deal of accuracy, especially if we had publicly announced that we would choose to one-box in such situations.
The genetic Newcomb requires an even more unrealistic scenario, since in the real world genes do not predict actions with anything close to 100...
I am currently learning about the basics of decision theory, most of which is common knowledge on LW. I have a question, related to why EDT is said not to work.
Consider the following Newcomblike problem: A study shows that most people who two-box in Newcomblike problems as the following have a certain gene (and one-boxers don't have the gene). Now, Omega could put you into something like Newcomb's original problem, but instead of having run a simulation of you, Omega has only looked at your DNA: If you don't have the "two-boxing gene", Omega puts $1M into box B, otherwise box B is empty. And there is $1K in box A, as usual. Would you one-box (take only box B) or two-box (take box A and B)? Here's a causal diagram for the problem:
Since Omega does not do much other than translating your genes into money under a box, it does not seem to hurt to leave it out:
I presume that most LWers would one-box. (And as I understand it, not only CDT but also TDT would two-box, am I wrong?)
Now, how does this problem differ from the smoking lesion or Yudkowsky's (2010, p.67) chewing gum problem? Chewing Gum (or smoking) seems to be like taking box A to get at least/additional $1K, the two-boxing gene is like the CGTA gene, the illness itself (the abscess or lung cancer) is like not having $1M in box B. Here's another causal diagram, this time for the chewing gum problem:
As far as I can tell, the difference between the two problems is some additional, unstated intuition in the classic medical Newcomb problems. Maybe, the additional assumption is that the actual evidence lies in the "tickle", or that knowing and thinking about the study results causes some complications. In EDT terms: The intuition is that neither smoking nor chewing gum gives the agent additional information.