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Misha comments on A model of UDT with a halting oracle - Less Wrong Discussion
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If every step in that code is valid, then that would work. In my opinion the shakiest step in your algorithm is the "Forall i" in the first line of A(). I'll probably reason myself into a hole if I try to figure out whether or not it's valid.
Well, at least in some cases (e.g., if A's code is equal to A_i's code) the proof is immediate. Proof is also possible for minor obvious modifications, like variable renaming, so the agent should still behave better than a quining agent for PD.
My goal for inventing this is to have a consistent agent that can know (can prove) its decision beforehand, at least sometimes, without getting into contradictions...