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jimmy comments on Eight Short Studies On Excuses - Less Wrong
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You wouldn't wish that you precommitted to cooperating iff you predicted that the other agent would cooperate iff he predicts that you will cooperate?
The problem is not cooperating conditionally on making that prediction. The problem is being able to make that prediction. TDT and UDT solve this by noting that it is the same algorithm making the decision for both agents.
Making the prediction is absolutely the hard part, but I still think that two agents using CDT with your precommitment strategy who are able to accurately predict would cooperate.
TDT/UDT do seem a bit more sophisticated, but I'm not solid enough on this decision theory thing to see where they advocated different decisions. I just don't think this is one of them.