Omega knows I’m smart enough to two box when I see that the #’s match up. So the # will be composite, thereby fulfilling his goal of predicting my actions and responding appropriately. The Lottery Bank doesn’t care about my decisions.
So I’ll two box.. I’ll do so, and would predictably do so. So Omega has selected a composite #, and I receive 1000$ from the boxes. Since its the same # the lottery will give me 2 million dollars.
But in this example Omega has already selected 1033, a prime, which means Omega already knows you will one-box. If it were me, how I would switch from your optimal strategy to deterministically one-boxing before even knowing whether the number is a prime (I didn’t know until I looked up; I’m speaking from the morgue right now) is beyond me.
I guess the lesson in this exercise is the same general argument Eliezer has made against lotteries: don’t bet on outcomes you don’t control.
Omega knows I’m smart enough to two box when I see that the #’s match up. So the # will be composite, thereby fulfilling his goal of predicting my actions and responding appropriately. The Lottery Bank doesn’t care about my decisions.
So I’ll two box.. I’ll do so, and would predictably do so. So Omega has selected a composite #, and I receive 1000$ from the boxes. Since its the same # the lottery will give me 2 million dollars.
But in this example Omega has already selected 1033, a prime, which means Omega already knows you will one-box. If it were me, how I would switch from your optimal strategy to deterministically one-boxing before even knowing whether the number is a prime (I didn’t know until I looked up; I’m speaking from the morgue right now) is beyond me.
I guess the lesson in this exercise is the same general argument Eliezer has made against lotteries: don’t bet on outcomes you don’t control.