I can’t cite sources off-hand but this suggestion is reasonably standard but taken to be a bit of a cheat (it dodges the difficult question). For this reason it is often stipulated that no objective chance device is available to the agent or that the predictor does something truly terrible if the agent decides by such a device (perhaps takes back all the money in the boxes and the money in the agent’s bank account).
In other words, the question becomes one of “Omega has two boxes box A and box B, which it fills based on what it thinks you will do. Box A has $1000 and box B has either $0 or $1000000 depending on whether Omega predicts you will take both boxes or only box B, respectively. If Omega predicts that you will do your best to be unpredictable, it will do something bad to you. Should you take box A, box B, or try to be unpredictable?” That question doesn’t seem as interesting.
I can’t cite sources off-hand but this suggestion is reasonably standard but taken to be a bit of a cheat (it dodges the difficult question). For this reason it is often stipulated that no objective chance device is available to the agent or that the predictor does something truly terrible if the agent decides by such a device (perhaps takes back all the money in the boxes and the money in the agent’s bank account).
Usually, it’s just “choosing using a randomizing device will be treated the same as two-boxing.”
In other words, the question becomes one of “Omega has two boxes box A and box B, which it fills based on what it thinks you will do. Box A has $1000 and box B has either $0 or $1000000 depending on whether Omega predicts you will take both boxes or only box B, respectively. If Omega predicts that you will do your best to be unpredictable, it will do something bad to you. Should you take box A, box B, or try to be unpredictable?” That question doesn’t seem as interesting.