Quantum coinflips work even if Omega can predict them. It’s like a branch-both-ways instruction. Just measure some quantum variable, then measure a noncommuting variable, and voila, you’ve been split into two or more branches that observe different results and thus can perform different strategies. Omega’s perfect predictor tells it that you will do both strategies, each with half of your original measure. There is no arrangement of atoms (encoding the right answer) that Omega can choose in advance that would make both of you wrong.
If Omega wants to smack down the use of randomness, I can’t stop it. But there are a number of game theoretic situations where the optimal response is random play, and any decision theory that can’t respond correctly is broken.
Quantum coinflips work even if Omega can predict them. It’s like a branch-both-ways instruction. Just measure some quantum variable, then measure a noncommuting variable, and voila, you’ve been split into two or more branches that observe different results and thus can perform different strategies. Omega’s perfect predictor tells it that you will do both strategies, each with half of your original measure. There is no arrangement of atoms (encoding the right answer) that Omega can choose in advance that would make both of you wrong.
I agree, and for this reason whenever I make descriptions I make Omega’s response to quantum smart-asses and other randomisers explicit and negative.
If Omega wants to smack down the use of randomness, I can’t stop it. But there are a number of game theoretic situations where the optimal response is random play, and any decision theory that can’t respond correctly is broken.