Thanks, this looks mostly right to me. Non-oracle algorithms with time limits were actually the first formulation we came up with, and then the oracle setting was mostly motivated by trying to devise an algorithm that didn’t have an arbitrary time limit. So it might be fruitful to try and remove the time limit from your idea too.
I wonder if there’s some way to maximize utility “implicitly” without having to mention concrete values in the proofs, e.g. by trying to prove statements of the form “if one-boxing leads to some unknown utility U, then two-boxing leads to utility less than U”. This exact form doesn’t seem to work, but maybe something similar can be made to work? Or if it can’t be made to work, maybe there’s some nice impossibility result lurking around the corner? Thanks for taking the time to think about this.
Thanks, this looks mostly right to me. Non-oracle algorithms with time limits were actually the first formulation we came up with, and then the oracle setting was mostly motivated by trying to devise an algorithm that didn’t have an arbitrary time limit. So it might be fruitful to try and remove the time limit from your idea too.
I wonder if there’s some way to maximize utility “implicitly” without having to mention concrete values in the proofs, e.g. by trying to prove statements of the form “if one-boxing leads to some unknown utility U, then two-boxing leads to utility less than U”. This exact form doesn’t seem to work, but maybe something similar can be made to work? Or if it can’t be made to work, maybe there’s some nice impossibility result lurking around the corner? Thanks for taking the time to think about this.