The "best predictor is malicious optimiser" problem

I don't have anything mathematical to say about this, but I imagined a human version. X asks Y for advice on some matter. Y has a motive for giving advice that X finds effective (it will improve his standing with X), but also has ulterior motives, that might or might not be to X's benefit. His advice will be selected to be effective for both solving X's problem and advancing Y's personal agenda, but perhaps less effective for the former than if the latter had not been a consideration.

Imagine a student asking a professor for career advice, and the professor suggesting the student do a Ph.D. with him. Will the student discover he's just paperclipping for the professor, and would have been better off accepting his friend's offer of co-founding a startup? But that friend has an agenda also.

What came to mind for me before reading the spoiler-ed options, was a variation on #2, with the difference being that, instead of trying to extract P's hypothesis about B, we instead modify T to get a T' which has P replaced with a P' which is a paperclip minimizer instead of maximizer, and then run both, and only use the output when the two agree, or if they give probabilities, use the average, or whatever.

Perhaps this could have an advantage over #2 if it is easier to negate what P is optimizing for than to extract P's model of B. (edit: though, of course, if extracting the model from P is feasible, that would be better than the scheme I described)

On the other hand, maybe this could still be dangerous, if P and P' have shared instrumental goals with regards to your predictions for B?

Though, if P has a good model of you, A, then presumably if you were to do this, both P and P' would expect you would do this, and, so I don't know what would make sense for them to do?

It seems like they would both expect that, while they may be able to influence you, that insofar as the influence would effect the expected value of number of paperclips, it would be canceled out by the other's influence (assuming that the ability to influence # paperclips via changing your prediction of B, is symmetric, which, I guess it might not be..).

I suppose this would be a reason why P would want its thought processes to be inscrutable to those simulating it, so that the simulators are unable to construct P' .

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As a variation on #4, if P is running on a computer in a physics simulation in T, then almost certainly a direct emulation of that computer running P would run faster than T does, and therefore whatever model of B that P has, can be computed faster than T can be. What if, upon discovering this fact about T, we restrict the search among Turing machines to only include machines that run faster than T?

This would include emulations of P, and would therefore include emulations of P's model of B (which would probably be even faster than emulating P?), but I imagine that a description of an emulation of P without the physics simulation and such would have a longer description than a description of just P's model of B. But maybe it wouldn't.

Typo? " A is aware that getting caught out making wrong predictions will lower its standing as a good hypothesis with A. "

Looks like you're making a logical error. Creating a machine that solves the halting problem is prohibited by logic. For many applications assuming a sufficiently powerful and logically consistent oracle is good enough but precisely these kinds of games you are playing, where you ask a machine to predict its own output/the output of a system involving itself, are where you get logically inconsistent. Indeed, imagine asking the oracle to simulate an equivalent version of itself and to output the the opposite answer to what its simulation outputs. This may seem like a derived question, but most "interesting" self-referential questions boil down to an instance of this. I think once you fix the logical inconsistency, you're left with an equivalent problem to AI in a box: boxed AI P is stronger that friendly AI A but has an agenda.

Alternatively, if you're assuming A is itself un-aligned (rather than friendly) and has the goal of getting the right answer at any cost then it looks like you need some more assumptions on A's structure. For example if A is sufficiently sophisticated and knows it has access to a much more powerful but untrustwothy oracle it might know to implement a merlin-arthur protocol.