Free will is not imcompatible with Omega predicting your actions(Well, unless Omega delibrately manipulates your actions based on that predictive power, but it’s outside the scope of this paradox), and Omega doesn’t even need to see inside your head, just observe your behavior until it thinks it can predict your decisions with high accuracy only based on the input that you have received. Omega doesn’t need to be 100% accurate anyway, only do better than 99,9%. Determinism is also not required, for the same reason.(Though yeah, you could toss a quantum coin to make the odds 50-50, but this seems a bit uninteresting case. Omega could predict that you select either at 50% chance, and thus you lose on average about 750 000$ every time Omega makes this offer to you.)
So basically, where we disagree is that Omega can choose first and you’d still have to one-box, since Omega knows the factors that correlate with your decision at high probability. Without breaking causality, without messing with free will and even without requiring determinism.
Free will is not imcompatible with Omega predicting your actions(Well, unless Omega delibrately manipulates your actions based on that predictive power, but it’s outside the scope of this paradox), and Omega doesn’t even need to see inside your head, just observe your behavior until it thinks it can predict your decisions with high accuracy only based on the input that you have received. Omega doesn’t need to be 100% accurate anyway, only do better than 99,9%. Determinism is also not required, for the same reason.(Though yeah, you could toss a quantum coin to make the odds 50-50, but this seems a bit uninteresting case. Omega could predict that you select either at 50% chance, and thus you lose on average about 750 000$ every time Omega makes this offer to you.)
So basically, where we disagree is that Omega can choose first and you’d still have to one-box, since Omega knows the factors that correlate with your decision at high probability. Without breaking causality, without messing with free will and even without requiring determinism.