The XOR blackmail problem allows Decision Theory agents to be money-pumped.
Say Omega, a perfectly honest perfect predictor of your actions, sends you the following message: "I have sent you this message iff your house has been infested with termites xor you will pay me $1000", and that a termite infestation would cost $1000000, a larger number.
A CDT agent reasons that whether they pay Omega has no causal influence on whether their house is infested with termites, and so elects to not pay Omega. Omega predicts this, so
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