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Vladimir_Nesov comments on Decision Theory Paradox: PD with Three Implies Chaos? - Less Wrong
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Right, for TDT agents to expect each other acting identically from the symmetry argument, we need to be able to permute not just places of TDT agents in the game, but also simultaneously places of TDT agents in TDT agents' utility functions without changing the game, which accomodates the difference in agents' utility functions.