Now, the NAN diagonalization can be solved if we assume the agent has access to random bits which are common between all of its copies but inaccessible by the rest of the universe (Omega). This assumption can be interpreted to mean the precursor gives the agent a randomly generated “password” before Omega copies it.
Sure, but this defeats the purpose of Omega being a predictor.
Not really. The idea is looking for a decision theory that performs optimally a natural class of problems which is as wide as possible. CDT is optimal for action-determined problems, UDT is supposed to be optimal for decision-determined problems. Allowing this use of randomness still leaves us with a class of problems much wider than action-determined: for example the Newcomb problem!
Sure, but this defeats the purpose of Omega being a predictor.
Not really. The idea is looking for a decision theory that performs optimally a natural class of problems which is as wide as possible. CDT is optimal for action-determined problems, UDT is supposed to be optimal for decision-determined problems. Allowing this use of randomness still leaves us with a class of problems much wider than action-determined: for example the Newcomb problem!