“I just flipped a fair coin. I decided, before I flipped the coin, that if it came up heads, I would ask you for $1000. And if it came up tails, I would give you $1,000,000 if and only if I predicted that you would give me $1000 if the coin had come up heads. The coin came up heads—can I have $1000?”
Err… pardon my noobishness but I am failing to see the game here. This is mostly me working it out audibly.
A less Omega version of this game involves flipping a coin, getting $100 on tails, losing $1 on heads. Using humans, it makes sense to have an arbiter holding $100 from the Flipper and $1 from the Guesser. With this setup, the Guesser should always play.
If the Flipper is Omega and offered the same game with the same fair arbiter there is no reason to not play. If Omega was a perfect predictor and knew what the coin would do before flipping it, should we play? If Omega commits to playing the game regardless of the prediction, yes, we should play.
If the arbiter is removed and Omega stands in as the arbiter, we should still play because it is assumed that Omega is honest and will pay out if tails appears. Even if we prepay before the coin flip, we should still play.
If the Flipper flips the coin before we prepay the arbiter, it should not matter. This is equivalent to the scenario of Omega being a perfect predictor.
The only two changes remaining are:
Us knowing the coin flip before we agree to play
Us not paying before we see the coin flip
The latter assumes we could renege on payment after seeing the coin but I highly doubt Omega would play the game with someone like this since this would be known to a perfect predictor. This means we can completely eliminate the arbiter.
This leaves us at the following scenario:
I just flipped a fair coin. I decided, before I flipped the coin, that if it came up heads, I would ask you for $1000. And if it came up tails, I would give you $1,000,000 if and only if I predicted that you would give me $1000 if the coin had come up heads. I know the result of the coin but will wait for you to agree to the game before I tell you what it is. Do you want to play?
The answer is “Yes.” Why does it matter if Omega blurts out the answer beforehand? Because we know we will “lose”?
In my opinion this is a trivial problem. If we assume that Omega is (a) fair and (b) accurate we would always play the game. Omega is predefined to not take advantage of us. We just got unlucky, which is perfectly acceptable as long as we do not know the answer beforehand.
So… what am I missing? It seems like there is mental warning when imagining myself before Omega and handing him $1000 when I “never had a shot”. But I did have a shot. I would never pay anyone other than Omega, but I am assuming Omega is being completely honest.
Why would anyone answer “No”? The basic answer, “Because you do not want to lose $1000″ seems completely irrational to me. I can see why it would appear rational, but Omega’s definition makes it irrational.
Err… pardon my noobishness but I am failing to see the game here. This is mostly me working it out audibly.
A less Omega version of this game involves flipping a coin, getting $100 on tails, losing $1 on heads. Using humans, it makes sense to have an arbiter holding $100 from the Flipper and $1 from the Guesser. With this setup, the Guesser should always play.
If the Flipper is Omega and offered the same game with the same fair arbiter there is no reason to not play. If Omega was a perfect predictor and knew what the coin would do before flipping it, should we play? If Omega commits to playing the game regardless of the prediction, yes, we should play.
If the arbiter is removed and Omega stands in as the arbiter, we should still play because it is assumed that Omega is honest and will pay out if tails appears. Even if we prepay before the coin flip, we should still play.
If the Flipper flips the coin before we prepay the arbiter, it should not matter. This is equivalent to the scenario of Omega being a perfect predictor.
The only two changes remaining are:
Us knowing the coin flip before we agree to play
Us not paying before we see the coin flip
The latter assumes we could renege on payment after seeing the coin but I highly doubt Omega would play the game with someone like this since this would be known to a perfect predictor. This means we can completely eliminate the arbiter.
This leaves us at the following scenario:
The answer is “Yes.” Why does it matter if Omega blurts out the answer beforehand? Because we know we will “lose”?
In my opinion this is a trivial problem. If we assume that Omega is (a) fair and (b) accurate we would always play the game. Omega is predefined to not take advantage of us. We just got unlucky, which is perfectly acceptable as long as we do not know the answer beforehand.
So… what am I missing? It seems like there is mental warning when imagining myself before Omega and handing him $1000 when I “never had a shot”. But I did have a shot. I would never pay anyone other than Omega, but I am assuming Omega is being completely honest.
Why would anyone answer “No”? The basic answer, “Because you do not want to lose $1000″ seems completely irrational to me. I can see why it would appear rational, but Omega’s definition makes it irrational.
See counterfactual mugging for an extended discussion in comments.
Thanks.