Quantum juju has nothing to do with decision theory. I guess I should have included it in the post about common mistakes. What would you say about this problem if you lived in a deterministic universe and never heard about quantum physics? You know that boundedly rational agents in such universes can observe things that look awfully similar to random noise, right?
Well, tossing a quantum coin is a simple way to provably sever causal links. In a deterministic universe with boundedly rational agents, I suppose, there could be cryptographical schemes producing equivalent guarantees.
What if I reformulate as follows: Omega says that it tossed a coin and so chose to check either the oddness or the evenness of the millionth digit of pi. Coin indicated the “oddness”, so bla bla bla.
The properties of the problem appear the same as the logical-coin CM, except now the possible causal influence from Omega is severed.
If I’m Omega, and I decide to check whether the 10^10 th digit of pi is 0, 2 or 5, and reward you if it is… how would you feel about that? I chose those numbers because we have ten fingers, and I chose reward because “e” is the 5th letter in the alphabet (I went through the letters of “reward” and “punish” until I found one that was the 10th (J), 5th (E) or 2nd (B) letter).
Or a second variant: I implement the logical-coin CM that can be described in python in the most compact way.
If it’s true that you chose the numbers because we have ten fingers (and because of nothing else), and I can verify that, then I feel I should behave as if the event is random with probability 0.3, even if it was the 10-th digit of pi, not 10^10-th.
I never had anything against logical uncertainty :)
The point, though, is that this setup—where I can verify Omega’s honest attempt at randomness—does not produce the paradoxes. In particular, it does not allow someone to pump money out of me. And so it seems to me that I can and should “keep paying up in Counterfactual Mugging even when the logical coinflip looks as obvious as 2+2=4.”
Quantum juju has nothing to do with decision theory. I guess I should have included it in the post about common mistakes. What would you say about this problem if you lived in a deterministic universe and never heard about quantum physics? You know that boundedly rational agents in such universes can observe things that look awfully similar to random noise, right?
Well, tossing a quantum coin is a simple way to provably sever causal links. In a deterministic universe with boundedly rational agents, I suppose, there could be cryptographical schemes producing equivalent guarantees.
What if I reformulate as follows: Omega says that it tossed a coin and so chose to check either the oddness or the evenness of the millionth digit of pi. Coin indicated the “oddness”, so bla bla bla.
The properties of the problem appear the same as the logical-coin CM, except now the possible causal influence from Omega is severed.
If I’m Omega, and I decide to check whether the 10^10 th digit of pi is 0, 2 or 5, and reward you if it is… how would you feel about that? I chose those numbers because we have ten fingers, and I chose reward because “e” is the 5th letter in the alphabet (I went through the letters of “reward” and “punish” until I found one that was the 10th (J), 5th (E) or 2nd (B) letter).
Or a second variant: I implement the logical-coin CM that can be described in python in the most compact way.
If it’s true that you chose the numbers because we have ten fingers (and because of nothing else), and I can verify that, then I feel I should behave as if the event is random with probability 0.3, even if it was the 10-th digit of pi, not 10^10-th.
Yep—welcome to logical uncertainty!
I never had anything against logical uncertainty :)
The point, though, is that this setup—where I can verify Omega’s honest attempt at randomness—does not produce the paradoxes. In particular, it does not allow someone to pump money out of me. And so it seems to me that I can and should “keep paying up in Counterfactual Mugging even when the logical coinflip looks as obvious as 2+2=4.”