I wasn’t sure if it’s really useful to think about value being linear in resources on some views. If you have a fixed population and imagine increasing the resources they have available, I assume that the value of the outcome is a strictly concave function of the resource base. Doubling the population might double the value of the outcome, although it’s not clear that this constitutes a doubling of resources. And why should it matter if the relationship between value and resources is strictly concave? Isn’t the key question something like whether there are potentially realizable futures that are many orders of magnitude more valuable than the default or where we are now? Answering yes seems compatible with thinking that the function relating resources to value is strictly concave and asymptotes, so long as it asymptotes somewhere suitably high up on the scale of value.
If you have a fixed population and imagine increasing the resources they have available, I assume that the value of the outcome is a strictly concave function of the resource base.
Certainly given current levels of technology, but perhaps not given future technology (e.g. indefinite life-extension technology), at least if individual wellbeing is proportional to number of happy years lived.
”Doubling the population might double the value of the outcome, although it’s not clear that this constitutes a doubling of resources.”
I was thinking you’d need twice as many resources to have twice as many people?
”And why should it matter if the relationship between value and resources is strictly concave? Isn’t the key question something like whether there are potentially realizable futures that are many orders of magnitude more valuable than the default or where we are now? Answering yes seems compatible with thinking that the function relating resources to value is strictly concave and asymptotes, so long as it asymptotes somewhere suitably high up on the scale of value. “
Yes, in principle, but I think that if you have the upper-bound view, then you do so on the basis of common-sense intuition. But if so, then I think the upper bound is probably really low in cosmic scales—like, if we already have a Common Sense Eutopia within the solar system, I think we’d be more than 50% of the way from 0 to the upper bound.
Another reason you might have an upper bound is that the axioms of expected utility theory require your utility function to be bounded given the most natural generalization to the case of countably infinite gambles.
I wasn’t sure if it’s really useful to think about value being linear in resources on some views. If you have a fixed population and imagine increasing the resources they have available, I assume that the value of the outcome is a strictly concave function of the resource base. Doubling the population might double the value of the outcome, although it’s not clear that this constitutes a doubling of resources. And why should it matter if the relationship between value and resources is strictly concave? Isn’t the key question something like whether there are potentially realizable futures that are many orders of magnitude more valuable than the default or where we are now? Answering yes seems compatible with thinking that the function relating resources to value is strictly concave and asymptotes, so long as it asymptotes somewhere suitably high up on the scale of value.
Certainly given current levels of technology, but perhaps not given future technology (e.g. indefinite life-extension technology), at least if individual wellbeing is proportional to number of happy years lived.
”Doubling the population might double the value of the outcome, although it’s not clear that this constitutes a doubling of resources.”
I was thinking you’d need twice as many resources to have twice as many people?
”And why should it matter if the relationship between value and resources is strictly concave? Isn’t the key question something like whether there are potentially realizable futures that are many orders of magnitude more valuable than the default or where we are now? Answering yes seems compatible with thinking that the function relating resources to value is strictly concave and asymptotes, so long as it asymptotes somewhere suitably high up on the scale of value. “
Yes, in principle, but I think that if you have the upper-bound view, then you do so on the basis of common-sense intuition. But if so, then I think the upper bound is probably really low in cosmic scales—like, if we already have a Common Sense Eutopia within the solar system, I think we’d be more than 50% of the way from 0 to the upper bound.
Another reason you might have an upper bound is that the axioms of expected utility theory require your utility function to be bounded given the most natural generalization to the case of countably infinite gambles.
Agreed!