It’s been pointed out I’m not really addressing what’s wrong with the two arguments which give you different “correct” choices for the Newcomb scenario. So here we go…

Expected Outcome
This argument assumes that the predictor has foreseen our choice [with high probability]. If however we assume that free willed choices are by definition unpredictable, this is a logical impossibility.

Dominant Outcome
This argument assumes that the choice we make is not correlated with the predictor’s choice, because that would involve reverse causation. However, if we assume that we’re not free willed, or that freely willed choices can be predicted (whatever that would involve), then there’s a common cause: Our mind’s tendency to select choice X in the scenario causes both our selection of X when we’re in the scenario and the predictor to anticipate this selection. So, our choice wouldn’t be independent of the predictor’s, and dominance wouldn’t hold.