In the first version, there's no causal relation between your choice and the number of people in the world. In the third, there is, and in the middle one, anthropics must also be considered.
I gave multiple scenarios to make this point.
If the predictor in newcomb doesn't touch the boxes but just tells you that they predict your choice is the same as what's in the box, it turns into the smoking lesions scenario.
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?