If they give in, they have not successfully precommitted. Now, you could argue that successfully precommitting is impossible. But in the Newcombian problem, it doesn't seem to be.
In the Lesion problem, the problem involves what essentially amounts to brain-damage, which gives a clear reason why precommitment is impossible.
Precommitting not to smoke also changes my disposition regarding smoking. I still might find it irresistable later.
This misses the point. If precommitting changes your disposition, and your disposition decides the outcome, precommitting is worthwhile.
If precommitting changes your disposition, and a lesion decides the outcome, precommitting is irrelevant.
Actually, talking about precommitting is any case a side issue, because it happens before the start of the game. We can just assume you've never thought it before Omega comes up to you, says that it has predicted your decision, and tells you the rules. Now what do you do?
In this case the situation is clearly the same as the lesion, and the lines of causality are the same: both your present disposition, and the million in the box, have a common cause, namely your previous disposition, but you can do nothing about it.
If you should one-box here, then you should not smoke in the lesion case.
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