The debate over Newcomblike decision problems turns out to revolve around the question of how to formally define "The probability of an outcome, conditioned on choice X" within calculations of expected utility\.
Probability theory already tells you how to define that. There are no degrees of freedom left once you've defined the outcome and conditioning information. The only possible area of debate is over what specific information we are conditioning on. If two different analyses get different answers, and they're both using probability theory correctly, then they must be conditioning on DIFFERENT information.