Yes, you would expect that you would find yourself handing over the money. If told “Omega will soon predict that you will give him $5”, then you divide the universe into two categories—I will give over $5, or I won’t—and assign much greater probability to the first option.
But that is not a reason to give him $5 if you otherwise wouldn’t. It’s a reason to expect that there will compelling reasons to make you do it—but if these compelling reasons don’t materialise, there is no reason for you to act as if they were there.
Yes, you would expect that you would find yourself handing over the money. If told “Omega will soon predict that you will give him $5”, then you divide the universe into two categories—I will give over $5, or I won’t—and assign much greater probability to the first option.
But that is not a reason to give him $5 if you otherwise wouldn’t. It’s a reason to expect that there will compelling reasons to make you do it—but if these compelling reasons don’t materialise, there is no reason for you to act as if they were there.
Yes, I agree with this.