Hmm. Then I’m not sure I agree. When I think of prototypical example scenarios of “business as usual but with more total capital” I kind of agree that they seem less valuable than +20%. But on the other hand, I feel like if I tried to come up with some first-principle-based ‘utility function’ I’d be surprised if it had returns than diminish much more strongly than logarithmic. (That’s at least my initial intuition—not sure I could justify it.) And if it was logarithmic, going from $10B to $100B should add about as much value than going from $1B to $10B, and I feel like the former adds clearly more than 20%.
(I guess there is also the question what exactly we’re assuming. E.g., should the fact that this additional $100B donor appears also make me more optimistic about the growth and ceiling of total longtermist-aligned capital going forward? If not, i.e. if I should compare the additional $100B to the net present expected value of all longtermist capital that will ever appear, then I’m much more inclined to agree with “business as usual + this extra capital adds much less than 20%”. In this latter case, getting the $100B now might simply compress the period of growth of longtermist capital from a few years or decades to a second, or something like that.)
OK, on a second thought I think this argument doesn’t work because it’s basically double-counting: the reason why returns might not diminish much faster than logarithmic may be precisely that new, ‘crazy’ opportunities become available.
A production function roughly along the lines of utility = funding ^ 0.2 * talent ^ 0.6 (this has diminishing returns to funding*talent, but the returns diminish slowly)
A default assumption that longtermism will eventually end up with $30-$300B in funding, let’s assume $100B
Increasing the funding from $100B to $200B would then increase utility by 15%.
Hmm. Then I’m not sure I agree. When I think of prototypical example scenarios of “business as usual but with more total capital” I kind of agree that they seem less valuable than +20%. But on the other hand, I feel like if I tried to come up with some first-principle-based ‘utility function’ I’d be surprised if it had returns than diminish much more strongly than logarithmic. (That’s at least my initial intuition—not sure I could justify it.) And if it was logarithmic, going from $10B to $100B should add about as much value than going from $1B to $10B, and I feel like the former adds clearly more than 20%.
(I guess there is also the question what exactly we’re assuming. E.g., should the fact that this additional $100B donor appears also make me more optimistic about the growth and ceiling of total longtermist-aligned capital going forward? If not, i.e. if I should compare the additional $100B to the net present expected value of all longtermist capital that will ever appear, then I’m much more inclined to agree with “business as usual + this extra capital adds much less than 20%”. In this latter case, getting the $100B now might simply compress the period of growth of longtermist capital from a few years or decades to a second, or something like that.)
OK, on a second thought I think this argument doesn’t work because it’s basically double-counting: the reason why returns might not diminish much faster than logarithmic may be precisely that new, ‘crazy’ opportunities become available.
Here’s a toy model:
A production function roughly along the lines of utility = funding ^ 0.2 * talent ^ 0.6 (this has diminishing returns to funding*talent, but the returns diminish slowly)
A default assumption that longtermism will eventually end up with $30-$300B in funding, let’s assume $100B
Increasing the funding from $100B to $200B would then increase utility by 15%.