I think “maximising” still makes sense in one-shot problems. 2>1 and 1000>1, but it’s also the case that 1000>2, even without expected utility. The way I see it, EU is a method of comparing choices based on their average utility, but the “average” turns out to be a less useful metric when you only have one chance.
So for cases when an outcome is not a constant amount of paperclips we need more rules than what the object of attention is. So a paperclip maximiser is actually underspecified.
If this is true, it would imply that in a one-shot problem, a utility function is not enough on its own to determine what is the “optimal” choice when you want to “maximise” (get the highest value you can) on that utility function. This would be a pretty big result, I think.
I think that if there is a part that is underspecified, though, it’s not the paperclip maximiser, but the word “optimal”. What does it mean for a choice to be “optimal” relative to other choices, when it might turn out better or worse depending on luck? I haven’t been able to answer that question.
Many times opinions how to handle uncertainty get baked into the utility functions. That is a standard naive construction is to say “be risk neutral” and value paperclips linearly for their amount. But I could imagine a policy for which more paperclips is always better but from a default position of 100% 2 paperclips it wouldn’t choose a option of 0.1% 1 paperclips, 49.9% 2 paperclips and 50% 3 paperclips. One can construct a “risk averse” function where the new function can simply be optimised. But does it really mean the new function is not a paper clip maximation function?
You’re absolutely right. I was starting to get at this idea from another of the comments, but you’ve laid out where I’ve gone wrong very clearly. Thank you.
Very interesting, thank you!
I think “maximising” still makes sense in one-shot problems. 2>1 and 1000>1, but it’s also the case that 1000>2, even without expected utility. The way I see it, EU is a method of comparing choices based on their average utility, but the “average” turns out to be a less useful metric when you only have one chance.
If this is true, it would imply that in a one-shot problem, a utility function is not enough on its own to determine what is the “optimal” choice when you want to “maximise” (get the highest value you can) on that utility function. This would be a pretty big result, I think.
I think that if there is a part that is underspecified, though, it’s not the paperclip maximiser, but the word “optimal”. What does it mean for a choice to be “optimal” relative to other choices, when it might turn out better or worse depending on luck? I haven’t been able to answer that question.
Many times opinions how to handle uncertainty get baked into the utility functions. That is a standard naive construction is to say “be risk neutral” and value paperclips linearly for their amount. But I could imagine a policy for which more paperclips is always better but from a default position of 100% 2 paperclips it wouldn’t choose a option of 0.1% 1 paperclips, 49.9% 2 paperclips and 50% 3 paperclips. One can construct a “risk averse” function where the new function can simply be optimised. But does it really mean the new function is not a paper clip maximation function?
You’re absolutely right. I was starting to get at this idea from another of the comments, but you’ve laid out where I’ve gone wrong very clearly. Thank you.