In light of my earlier comment about logical induction, I think this case is different from the classical use-case for the principle of ignorance, where we have n that we know nothing about, and so we assign each probability 1/n. Here, we have a set of commitments that we know entails that there is either a strictly positive or an extreme, delta-function-like distribution over some variable X, but we don’t know which. So if we apply the principle of ignorance to those two possibilities, we end up assigning equal higher-order-credence to the normative proposition that we ought to assign a strictly positive distribution over X and to the proposition that we ought to assign a delta-function-distribution over X. If our final credal distribution over X is a blend of these two distributions, then we end up with a strictly positive credal distribution over X. But, now we’ve arrived at a conclusion that we stipulated might be inconsistent with our other epistemic commitments! If nothing else, this shows that applying indifference reasoning here is much more involved than in the classic case. Garrabrant wants to say, I think, that this reasoning could be fine as long as the inconsistency that it potentially leads to can’t be exploited in polynomial time. But then see my other worries about this kind of reasoning in my response above.
In light of my earlier comment about logical induction, I think this case is different from the classical use-case for the principle of ignorance, where we have n that we know nothing about, and so we assign each probability 1/n. Here, we have a set of commitments that we know entails that there is either a strictly positive or an extreme, delta-function-like distribution over some variable X, but we don’t know which. So if we apply the principle of ignorance to those two possibilities, we end up assigning equal higher-order-credence to the normative proposition that we ought to assign a strictly positive distribution over X and to the proposition that we ought to assign a delta-function-distribution over X. If our final credal distribution over X is a blend of these two distributions, then we end up with a strictly positive credal distribution over X. But, now we’ve arrived at a conclusion that we stipulated might be inconsistent with our other epistemic commitments! If nothing else, this shows that applying indifference reasoning here is much more involved than in the classic case. Garrabrant wants to say, I think, that this reasoning could be fine as long as the inconsistency that it potentially leads to can’t be exploited in polynomial time. But then see my other worries about this kind of reasoning in my response above.