I agree that this is what most people think, but it is a mistake.
I don't agree to leave Newcomb aside in considering this, because my position is that they are the same problem. If I have no choice in the smoking lesion, I have no choice in Newcomb.
Consider the Newcomb case.
I exist, and my brain and body are in a certain condition. I did not put them in that condition. I cannot make them not have been in that condition.
Omega looks at me. Using the condition of my brain and body -- conditions over which I have no control whatsoever -- he determines whether I am going to choose one box or two boxes. He has 100% accuracy, and this implies that the situation is completely determined by the condition of my brain and body.
In other words, "the condition of my brain and body" functions exactly like the lesion. It completely "predetermines" the outcome. If I have no choice in the lesion case, I have no choice in Newcomb.
Nonetheless, I say I have a choice in Newcomb, because the condition of my brain and body imply that I will engage in a certain process of reasoning, considering the alternatives of one boxing and two boxing, and choose one of them.
Likewise, I have a choice in the lesion case, because the lesion implies that I will engage in a certain process of reasoning, considering the alternatives of smoking and not smoking, and choose one of them.
In both cases, the outcome is predetermined. In both cases, the outcome is the result of a choice that results from a process of thought.
I don't agree to leave Newcomb aside in considering this, because my position is that they are the same problem.
If they are the same problem, you shouldn't care about leaving one aside. The smoking lesion is a simpler and clearer problem because it doesn't need to postulate a supernatural entity.
In other words, "the condition of my brain and body" functions exactly like the lesion. It completely "predetermines" the outcome.
So you're a determinist. OK.
...Nonetheless, I say I have a choice in Newcomb, because the condition of my bra
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?