I’m not sure the algorithm you describe here is necessarily outside current TDT though. The counterfactual still corresponds to an actual thing Omega simulated. It’d be more like this: Omega did not add the “you are wrong” prefix. Therefore, conditioning on the idea that Omega always tries simulating with that prefix and only states the prefix if I (or whoever Omega is offering the challenge to) was wrong in that simulation, the simulation in question then did not produce the wrong answer.
Therefore a sufficient property for a good answer (one with higher expected utility) is that it should have the same output as that simulation. Therefore determine what that output was...
ie, TDT shouldn’t have much more problem (in principle) with that than with being told that it needs to guess the Nth digit of Pi. If possible, it would simply compute the Nth digit of Pi. In this case, it has to simply compute the outcome of a certain different algorithm which happens to be equivalent to its own decision algorithm when faced with a certain situation. I don’t THINK this would be inherently outside of current TDT as I understand it
I may be completely wrong on this, though, but that’s the way it seems to me.
As far as stuff like the problem in the OP, I suspect though that the Right Way for dealing with things analogous to counterfactual mugging (and extended to the problem in the OP) and such amounts to a very general precommitment… Or a retroactive precommitment.
My thinking here is rather fuzzy. I do suspect though that the Right Way probably looks something like the the TDT, in advance, doing a very general precommitment to be the sort of being that tends to have high expected utility when faced with counterfactual muggers and whatnot… (Or retroactively deciding to be the sort of being that effectively has the logical implication of being mathematically “precommited” to be such.)
Fair enough.
I’m not sure the algorithm you describe here is necessarily outside current TDT though. The counterfactual still corresponds to an actual thing Omega simulated. It’d be more like this: Omega did not add the “you are wrong” prefix. Therefore, conditioning on the idea that Omega always tries simulating with that prefix and only states the prefix if I (or whoever Omega is offering the challenge to) was wrong in that simulation, the simulation in question then did not produce the wrong answer.
Therefore a sufficient property for a good answer (one with higher expected utility) is that it should have the same output as that simulation. Therefore determine what that output was...
ie, TDT shouldn’t have much more problem (in principle) with that than with being told that it needs to guess the Nth digit of Pi. If possible, it would simply compute the Nth digit of Pi. In this case, it has to simply compute the outcome of a certain different algorithm which happens to be equivalent to its own decision algorithm when faced with a certain situation. I don’t THINK this would be inherently outside of current TDT as I understand it
I may be completely wrong on this, though, but that’s the way it seems to me.
As far as stuff like the problem in the OP, I suspect though that the Right Way for dealing with things analogous to counterfactual mugging (and extended to the problem in the OP) and such amounts to a very general precommitment… Or a retroactive precommitment.
My thinking here is rather fuzzy. I do suspect though that the Right Way probably looks something like the the TDT, in advance, doing a very general precommitment to be the sort of being that tends to have high expected utility when faced with counterfactual muggers and whatnot… (Or retroactively deciding to be the sort of being that effectively has the logical implication of being mathematically “precommited” to be such.)