You are, in this very post, questing and saying that your utility function PROBABLY this and that you dont think there’s uncertainty about it… That is, you display uncertainty about your utility function. Check mate.
Also, “infinity=infinity” is not the case. Infinity ixs not a number, and the problem goes away if you use limits. otherwise, yes, I even probaböly have unbounded but very slow growing facotrs for s bunch of thigns like that.
You are, in this very post, questing and saying that your utility function PROBABLY this and that you dont think there’s uncertainty about it… That is, you display uncertainty about your utility function. Check mate.
Even if I was uncertain about my utility function, you’re still wrong. The factor you are forgetting about is uncertainty. With a bounded utility function infinite utility scores the same as a smaller amount of utility. So you should always assume a bounded utility function, because unbounded utility functions don’t offer any more utility than bounded ones and bounded ones outperform unbounded ones in situations like Pascal’s Mugging. There’s really no point to believing you have an unbounded function.
I just used the same logic you did. But the difference is that I assumed a bounded utility function was the default standard for comparison, whereas you assumed, for no good reason, that the unbounded one was.
I don’t know what the proper way to calculate utility when you are uncertain about your utility function. But I know darn well that doing an expected-utility calculation about what utility each function will yield and using one of the two functions that are currently in dispute to calculate that utility is a crime against logic. If you do that you’re effectively assigning “having an unbounded function” a probability of 1. And 1 isn’t a probability.
Your formulation of “unbounded utility function always scores infinity so it always wins” is not the correct way to compare two utility functions under uncertainty. You could just as easily say “unbounded and bounded both score the same, except in Pascal’s mugging where bounded scores higher, so bounded always wins.”
I think that using expected utility calculation might be valid for things like deciding whether you assign any utility at all to object or consequence. But for big meta-level questions about what your utility function even is attempting to use them is a huge violation of logic.
You are, in this very post, questing and saying that your utility function PROBABLY this and that you dont think there’s uncertainty about it… That is, you display uncertainty about your utility function. Check mate.
Also, “infinity=infinity” is not the case. Infinity ixs not a number, and the problem goes away if you use limits. otherwise, yes, I even probaböly have unbounded but very slow growing facotrs for s bunch of thigns like that.
Even if I was uncertain about my utility function, you’re still wrong. The factor you are forgetting about is uncertainty. With a bounded utility function infinite utility scores the same as a smaller amount of utility. So you should always assume a bounded utility function, because unbounded utility functions don’t offer any more utility than bounded ones and bounded ones outperform unbounded ones in situations like Pascal’s Mugging. There’s really no point to believing you have an unbounded function.
I just used the same logic you did. But the difference is that I assumed a bounded utility function was the default standard for comparison, whereas you assumed, for no good reason, that the unbounded one was.
I don’t know what the proper way to calculate utility when you are uncertain about your utility function. But I know darn well that doing an expected-utility calculation about what utility each function will yield and using one of the two functions that are currently in dispute to calculate that utility is a crime against logic. If you do that you’re effectively assigning “having an unbounded function” a probability of 1. And 1 isn’t a probability.
Your formulation of “unbounded utility function always scores infinity so it always wins” is not the correct way to compare two utility functions under uncertainty. You could just as easily say “unbounded and bounded both score the same, except in Pascal’s mugging where bounded scores higher, so bounded always wins.”
I think that using expected utility calculation might be valid for things like deciding whether you assign any utility at all to object or consequence. But for big meta-level questions about what your utility function even is attempting to use them is a huge violation of logic.