I think we need to remember here the difference between logical influence and causal influence?
My genes can cause me to be inclined towards smoking, and my genes can cause me to get lesions. If I choose to smoke, not knowing my genes, then that's evidence for what my genes say, and it's evidence about whether I'll get lesions; but it doesn't actually causally influence the matter.
My genes can incline me towards one-boxing, and can incline Omega towards putting $1M in the box. If I choose to two-box despite my inclinations, then that provides me with evidence about what Omega did, but it doesn't causally influence the matter.
If I don't know which of two worlds I'm in, I can't increase the probability of one by saying "in world A, I'm more likely to do X than in world B, so I'm going to do X". If nothing else, if I thought that worked, then I would do it whatever world I was in, and it would no longer be true.
In standard Newcomb, my inclination to one-box actually does make me one-box. In this version, my inclination to one-box is just a node that you've labelled "inclination to one-box", and you've said that Omega cares about the node rather than about whether or not I one-box. But you're still permitting me to two-box, so that node might just as well be "inclination to smoke".
In the original Newcomb's problem, am I allowed to say "in the world with the million, I am more likely to one-box than in the world without, so I'm going to one-box"? If I thought this worked, then I would do it no matter what world I was in, and it would no longer be true...
Except that it is still true. I can definitely reason this way, and if I do, then of course I had the disposition to one-box, and of course Omega put the million there; because the disposition to one-box was the reason I wanted to reason this way.
And likewise, in the genetic variant, I can reason this way, and it will still work, because the one-boxing gene is responsible for me reasoning this way rather than another way.
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.