Given how good Omega is at predicting people’s decisions, I should assume that a world where I choose to take both boxes cannot coincide with a world where Omega predicted I would only take one box. In other words, the payoff matrix that creates this paradox in the first place is an illusion, because the scenario in which you two-box and get $1,001,000 simply doesn’t exist. Or at the very least, it is so unlikely to exist that you should behave as though it doesn’t.
This is the way I think about it:
Given how good Omega is at predicting people’s decisions, I should assume that a world where I choose to take both boxes cannot coincide with a world where Omega predicted I would only take one box. In other words, the payoff matrix that creates this paradox in the first place is an illusion, because the scenario in which you two-box and get $1,001,000 simply doesn’t exist. Or at the very least, it is so unlikely to exist that you should behave as though it doesn’t.