Can utility go arbitrarily high? There are diminishing returns on almost every kind of good thing. I have difficulty imagining life with utility orders of magnitude higher than what we have now. Infinitely long youth might be worth a lot, but even that is only so many doublings due to discounting.
I’m curious why it’s getting downvoted without reply. Related thread here. How high do you think “utility” can go?
I would guess you’re being downvoted by someone who is frustrated not by you so much as by all the other people before you who keep bringing up diminishing returns even though the concept of “utility” was invented to get around that objection.
“Utility” is what you have after you’ve factored in diminishing returns.
We do have difficulty imagining orders of magnitude higher utility. That doesn’t mean it’s nonsensical. I think I have orders of magnitude higher utility than a microbe, and that the microbe can’t understand that. One reason we develop mathematical models is that they let us work with things that we don’t intuitively understand.
If you say “Utility can’t go that high”, you’re also rejecting utility maximization. Just in a different way.
Nothing about utility maximization model says utility function is unbounded—the only mathematical assumptions for a well behaved utility function are U’(x) >= 0, U″(x) ⇐ 0.
If the function is let’s say U(x) = 1 − 1/(1+x), U’(x) = (x+1)^-2, then it’s a properly behaving utility function, yet it never even reaches 1.
And utility maximization is just a model that breaks easily—it can be useful for humans to some limited extent, but we know humans break it all the time. Trying to imagine utilities orders of magnitude higher than current gets it way past its breaking point.
Nothing about utility maximization model says utility function is unbounded
Yep.
the only mathematical assumptions for a well behaved utility function are U’(x) >= 0, U″(x) ⇐ 0
Utility functions aren’t necessarily over domains that allow their derivatives to be scalar, or even meaningful (my notional u.f., over 4D world-histories or something similar, sure isn’t). Even if one is, or if you’re holding fixed all but one (real-valued) of the parameters, this is far too strong a constraint for non-pathological behavior. E.g., most people’s (notional) utility is presumably strictly decreasing in the number of times they’re hit with a baseball bat, and non-monotonic in the amount of salt on their food.
We could have a contest, where each contestant tries to describe a scenario that has the largest utility to a judge. I bet that after a few rounds of this, we’ll converge on some scenario of maximum utility, no matter who the judge is.
Does this show that utility can’t go arbitrarily high?
ETA: The above perhaps only shows the difficulty of not getting stuck in a local maximum. Maybe a better argument is that a human mind can only consider a finite subset of configuration space. The point in that subset with the largest utility must be the maximum utility for that mind.
Can utility go arbitrarily high? There are diminishing returns on almost every kind of good thing. I have difficulty imagining life with utility orders of magnitude higher than what we have now. Infinitely long youth might be worth a lot, but even that is only so many doublings due to discounting.
I’m curious why it’s getting downvoted without reply. Related thread here. How high do you think “utility” can go?
I would guess you’re being downvoted by someone who is frustrated not by you so much as by all the other people before you who keep bringing up diminishing returns even though the concept of “utility” was invented to get around that objection.
“Utility” is what you have after you’ve factored in diminishing returns.
We do have difficulty imagining orders of magnitude higher utility. That doesn’t mean it’s nonsensical. I think I have orders of magnitude higher utility than a microbe, and that the microbe can’t understand that. One reason we develop mathematical models is that they let us work with things that we don’t intuitively understand.
If you say “Utility can’t go that high”, you’re also rejecting utility maximization. Just in a different way.
Nothing about utility maximization model says utility function is unbounded—the only mathematical assumptions for a well behaved utility function are U’(x) >= 0, U″(x) ⇐ 0.
If the function is let’s say U(x) = 1 − 1/(1+x), U’(x) = (x+1)^-2, then it’s a properly behaving utility function, yet it never even reaches 1.
And utility maximization is just a model that breaks easily—it can be useful for humans to some limited extent, but we know humans break it all the time. Trying to imagine utilities orders of magnitude higher than current gets it way past its breaking point.
Yep.
Utility functions aren’t necessarily over domains that allow their derivatives to be scalar, or even meaningful (my notional u.f., over 4D world-histories or something similar, sure isn’t). Even if one is, or if you’re holding fixed all but one (real-valued) of the parameters, this is far too strong a constraint for non-pathological behavior. E.g., most people’s (notional) utility is presumably strictly decreasing in the number of times they’re hit with a baseball bat, and non-monotonic in the amount of salt on their food.
We could have a contest, where each contestant tries to describe a scenario that has the largest utility to a judge. I bet that after a few rounds of this, we’ll converge on some scenario of maximum utility, no matter who the judge is.
Does this show that utility can’t go arbitrarily high?
ETA: The above perhaps only shows the difficulty of not getting stuck in a local maximum. Maybe a better argument is that a human mind can only consider a finite subset of configuration space. The point in that subset with the largest utility must be the maximum utility for that mind.