That is right—the choice does not determine the contents. But the choice is not as independent as common intuition suggests. Omega’s belief and your choice share common causes. Human decisions are caused—they don’t spontaneously spring from nowhere, causally unconnected to the rest of the universe—even if that’s how it sometimes feels from the inside. The situational state, and the state of your brain going into the situation, determine the decision that your brain will ultimately produce. Omega is presumed to know enough about these prior states, and how you function, to know what you will decide. Omega may well know better than you do what decision you will reach! It’s important to realize that this is not that far-fetched. Heck, that very thing sometimes happens between people who know each other very well, without the benefit of one of them being Omega! Your objection supposes that somehow, everything in the world, including your brain, could be configured so as to lead to a one-box decision; but then at the last moment, you could somehow pull a head-fake and just spontaneously spawn a trancendent decision-process that decides to two box. It might feel to you intuitively that humans can do this, but as far as we know they do not in fact possess that degree of freedom.
To summarize, Omega’s prediction and your decision have common, ancestor causes. Human decision-making feels transcendent from the inside, but is not literally so. Resist thinking of first-person choosing as some kind of prime mover.
That is right—the choice does not determine the contents. But the choice is not as independent as common intuition suggests. Omega’s belief and your choice share common causes. Human decisions are caused—they don’t spontaneously spring from nowhere, causally unconnected to the rest of the universe—even if that’s how it sometimes feels from the inside. The situational state, and the state of your brain going into the situation, determine the decision that your brain will ultimately produce. Omega is presumed to know enough about these prior states, and how you function, to know what you will decide. Omega may well know better than you do what decision you will reach! It’s important to realize that this is not that far-fetched. Heck, that very thing sometimes happens between people who know each other very well, without the benefit of one of them being Omega! Your objection supposes that somehow, everything in the world, including your brain, could be configured so as to lead to a one-box decision; but then at the last moment, you could somehow pull a head-fake and just spontaneously spawn a trancendent decision-process that decides to two box. It might feel to you intuitively that humans can do this, but as far as we know they do not in fact possess that degree of freedom.
To summarize, Omega’s prediction and your decision have common, ancestor causes. Human decision-making feels transcendent from the inside, but is not literally so. Resist thinking of first-person choosing as some kind of prime mover.