In the lesion case, I am assuming that the lesion has 100% chance of causing you to make a certain decision. If that is not assumed, we are not discussing the situation I am talking about.
So the causal process is like this:
I just simulated the lesion process by thinking about it. Omega does the same thing; the details of 2 are irrelevant, as long as we know that the lesion will cause a thought process that will cause smoking.
In the lesion case, I am assuming that the lesion has 100% chance of causing you to make a certain decision.
Sure.
Omega does the same thing; the details of 2 are irrelevant, as long as we know that the lesion will cause a thought process that will cause smoking.
The details of 2 is irrelevant, but the details of how Omage works are relevant. If Omega checks for the lesion, then your choice has no counterfactual causal effect on Omega. If Omega simulates your mind, then your choice does have a counterfactual causal effect.
Lesion -> thought process -...
You're given the option to torture everyone in the universe, or inflict a dust speck on everyone in the universe. Either you are the only one in the universe, or there are 3^^^3 perfect copies of you (far enough apart that you will never meet.) In the latter case, all copies of you are chosen, and all make the same choice. (Edit: if they choose specks, each person gets one dust speck. This was not meant to be ambiguous.)
As it happens, a perfect and truthful predictor has declared that you will choose torture iff you are alone.
What do you do?
How does your answer change if the predictor made the copies of you conditional on their prediction?
How does your answer change if, in addition to that, you're told you are the original?