I don't understand why the Smoking Lesion is a problem for evidential decision theory. I would simply accept that in the scenario given, you shouldn't smoke. And I don't see why you assert that this doesn't lessen your chances of getting cancer, except in the same sense that two-boxing doesn't lessen your chances of getting the million.
I would just say: in the scenario give, you should not smoke, and this will improve your chances of not getting cancer.
If you doubt this, consider if the correlation were known to be 100%; every person who ever smoked up til...
I see you've moved this discussion off-site. FWIW, I commend you for trying to organize the various decision theory issues into a more accessible and organized sequence. I'd like to suggest that you take some of this and use it to improve the (almost comically sparse) decision theory articles on the LW Wiki. If that's really going to be the go-to place for LW knowledge, your efforts to summarize and present this info could really be useful there, and any redundancy with existing blog posts would be a non-issue.
I'm confused as to why you said you weren't continuing this on Less Wrong, then posted it on Less Wrong.
I've read the smoking lesion thing before, and what occurred to be is that even under EDT, the reasoning in there is wrong. What I mean was that one shouldn't simply reason it out by comparing to the average stats, but take into account the fact that they're using EDT itself. ie, they should say "given that a person is using EDT, then what's the correlation between etc etc..."
Worth referencing:
The Smoking Lesion on the wiki.
Timeless Decision Theory and Meta-Circular Decision Theory, where Eliezer discusses this problem (among others)
(By the way, your blog has some interesting posts!)
EDIT - I had missed the full context as follows: "In my example, it is give that Omega decides what you are going to do, but that he causes you to do it in the same way you ordinarily do things, namely with some decision theory and by thinking some thoughts etc."
for the comment below, so I accept Kingreaper's reply here. BUT I will give another answer, below.
If the fact that Omega causes it means that you are irrational, then the fact that the laws of physics cause your actions also means that you are irrational. You are being inconsistent here.
"I mean my mind deciding what to do on the basis of it's own thought processes, out of set of possibilities that could be realised if my mind were different than it is."
so can we apply this to a chess program as you suggest? I'll rewrite it as:
"I mean a chess program deciding what to do on the basis of it's own algorithmic process, out of set of possibilities that could be realised if its algorithm were different than it is."
No problem there! So you didn't say anything untrue about chess programs.
BUT
"I, in this scenario, cannot. No matter how my mind was setup prior to the scenario, there is only one possible outcome."
This doesn't make sense at all. The scenario requires your mind to be set up in a particular way. This does not mean that if your mind were set up in a different way you would still behave in the same way: If your mind were set up in a different way, either the outcome would be the same or your mind would be outside the scope of the scenario.
We can do exactly the same thing with a chess program.
Suppose I get a chess position (the state of play in a game) and present it to a chess program. The chess program replies with the move "Ngf3". We now set the chess position up the same way again, and we predict that the program will move "Ngf3" (because we just saw it do that with this position.) As far as we are concerned, the program can't do anything else. As predicted, the program moves "Ngf3". Now, the program was required by its own nature to make that move. It was forced to make that move by the way that the computer code in the program was organized, and by the chess position itself. We could say that even if the program had been different, it would still have made the same move - but this would be a fallacy, because if the program were different in such a way as to cause it to make a different move, it could never be the program about which we made that prediction. It would be a program about which a different prediction would be needed. Likewise, saying that your mind is compelled to act in a certain way, regardless of how it is set up, is also a fallacy, because the situation describes your mind as having set up in a specific way, just like the program with the predicted chess move, and if it wasn't it would be outside the scope of the prediction.
"I, in this scenario, cannot. No matter how my mind was setup prior to the scenario, there is only one possible outcome."
This doesn't make sense at all. The scenario requires your mind to be set up in a particular way. This does not mean that if your mind were set up in a different way you would still behave in the same way: If your mind were set up in a different way, either the outcome would be the same or your mind would be outside the scope of the scenario.
No matter how my mind is set-up, Omega will change the scenario it to produce the sa...
This is part of a sequence titled "An introduction to decision theory". The previous post was Newcomb's Problem: A problem for Causal Decision Theories
For various reasons I've decided to finish this sequence on a seperate blog. This is principally because there were a large number of people who seemed to feel that this sequence either wasn't up to the Less Wrong standard or felt that it was simply covering ground that had already been covered on Less Wrong.
The decision to post it on another blog rather than simply discontinuing it came down to the fact that other people seemed to feel that the sequence had value. Those people can continue reading it at "The Smoking Lesion: A problem for evidential decision theory".
Alternatively, there is a sequence index available: Less Wrong and decision theory: sequence index