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TobyBartels comments on You're in Newcomb's Box - Less Wrong
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The 'Azathoth problem' is isomorphic to the smoking lesion problem, which is not isomorphic to Newcomb's problem.
Hence, any decision theory capable of both (i) one-boxing in Newcomb's problem and (ii) choosing to smoke in the 'smoking lesion' problem will have no difficulty here.
EDIT: I'd better sketch out this "isomorphism": "smoking" = "acting virtuously, in defiance of our evolutionary drives", "not smoking" = "giving in to our instincts and trying to optimize number of children". "having the lesion" = "carrying genes that predispose you to virtuous behaviour, and therefore having a smaller chance of having been born in the first place", "not having the lesion" = "carrying genes that predispose you to evolutionarily 'selfish' behaviour and therefore having a larger chance of having been born".
This reminds me of a discussion a while back where I was interpreting Calvinist predestination as equivalent to Newcomb and Eliezer was interpreting it as equivalent to Smoking Lesion.
I think the difference involves whether the state is linked to a single urge or input, or whether it's linked to your entire decision-making process.
In the smoking lesion problem, your genotype is linked to whether or not you feel an urge to smoke. Once you feel the urge, the interesting decision theoretic bit is done; you can then decide whether or not to smoke knowing that it can't possibly affect your genotype.
In Newcomb's problem, the money in the boxes is linked to your final decision, so changing your decision can (in theory) change the money you find in the box.
This seems more like Newcomb's to me in that whether or not your genes are passed on is linked to whether or not you ultimately decide to reproduce - so I think the Newcombness of the problem is legitimate.
Whether my genes are passed on after me is linked to whether I reproduce, much as (in the relevant versions of Newcomb) the money in Box B is linked to whether I take Box A. But whether my genes were passed on before me is not linked to whether I reproduced, much as (in the smoking-lesion problem) my cancer status is not linked to whether I smoke.
Think of this at the genetic level, not the personal level. Let's say you have a gene G, which affects decision-making about reproduction. If G causes people to decide not to reproduce, then your ancestors possessing gene G will have not reproduced and you won't exist. If G makes you decide to reproduce, then your ancestors will have reproduced and you will exist. If we interpret decisions as altering the output of the algorithm that produced them, then deciding not to reproduce can alter the effects of gene G and therefore affect your ancestors with the gene.
This is false.
Even though G causes people to decide not to reproduce, my ancestors possessing gene G still reproduced, and I do exist.