If Omega offered to give you 2^n utils with probability 1/n, what n would you choose?
To the extent the question is meaningful it is mostly a prompt for the definition of ‘utility’. With a sophisticated definition of ‘utility’ the answer is implicit in the question (“arbitrarily big or arbitrarily small”). If the ‘utility’ concept is taken to exclude preferences regarding risk then the question is arbitrary in the same sense that leaving out any other kind of preference from the utility function would be.
I should note that given my utility function I have a suspicion that particularly large values of n are not just physically impossible to achieve but conceptually impossible. That is, if ‘1 util’ is taken to be “1 dust spec that I can’t even feel removed from my eye right now” then even infinite universes could not satisfy me given n of 3^^^3, a googolplex or even a googol. ‘Utility’ is unbounded but there just isn’t anything in preferences that scales that far.
To the extent the question is meaningful it is mostly a prompt for the definition of ‘utility’. With a sophisticated definition of ‘utility’ the answer is implicit in the question (“arbitrarily big or arbitrarily small”). If the ‘utility’ concept is taken to exclude preferences regarding risk then the question is arbitrary in the same sense that leaving out any other kind of preference from the utility function would be.
I should note that given my utility function I have a suspicion that particularly large values of n are not just physically impossible to achieve but conceptually impossible. That is, if ‘1 util’ is taken to be “1 dust spec that I can’t even feel removed from my eye right now” then even infinite universes could not satisfy me given n of 3^^^3, a googolplex or even a googol. ‘Utility’ is unbounded but there just isn’t anything in preferences that scales that far.