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gjm comments on JFK was not assassinated: prior probability zero events - Less Wrong
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(I'm getting downvotes because The Person Formerly Known As Eugine_Nier doesn't like me and is downvoting everything I post.)
Yes, I agree that the utility-function hack isn't the same as altering the AI's prior. It's more like altering its posterior. But isn't it still true that the effects on its inferences (or, more precisely, on its effective inferences -- the things it behaves as if it believes) are the same as if you'd altered its beliefs? (Posterior as well as prior.)
If so, doesn't what I said follow? That is:
After witnessing the message being read, it would conclude Y happened, as P(Y|X and message read) is high. Before witnessing this, it wouldn't, because P(Y|X) is (presumably) very low.
I may be misunderstanding something, but it seems like what you just said can't be addressing the actual situation we're talking about, because nothing in it makes reference to the AI's utility function, which is the thing that gets manipulated in the schemes we're talking about.
(I agree that the AI's nominal beliefs might be quite different in the two cases, but the point of the utility-function hack is to make its actions correspond to a different set of beliefs. I'm talking about its actions, not about its purely-internal nominal beliefs.)
Let V be the set of worlds in which X happens. Let W be the set of worlds in which X and Y happens. Since Y is very unlikely, P(W)<<P(V) (however, P(W|message read) is roughly P(V|message read)). The AI gets utility u' = u|V (the utility in the non-V worlds is constant, which we may as well set to zero).
Then if the AI is motivated to maximise u' (assume for the moment that it can't affect the probability of X), it will assume it is in the set V, and essentially ignore W. To use your terminology, u(Z|X) is low or negative, u(Z|X,Y) is high, but P(Y|X)*u(Z|X,Y) is low, so it likely won't do Z.
Then, after it notices the message is read, it shifts to assuming Y happened - equivalently, that it is in the world set W. When doing so, it knows that it is almost certainly wrong - that it's more likely in a world outside of V entirely where neither X nor Y happened - but it still tries, on the off-chance that it's in W.
However, since it's an oracle, we turn it off before that point. Or we use corrigibility to change its motivations.
Again, maybe I'm misunderstanding something -- but it sounds as if you're agreeing with me: once the AI observes evidence suggesting that its message has somehow been read, it will infer (or at least act as if it has inferred) Y and do Z.
I thought we were exploring a disagreement here; is there still one?
I think there is no remaining disagreement - I just want to emphasise that before the AI observes such evidence, it will behave the way we want.