Just to complement Khorton’s answer: With a discount rate of d [1], and a steady-state population of N, and a willingness to pay of $X, the total value of the future is N∗$X/d, so the willingness to pay for 0.01% of it would be 0.01∗N∗$X/d
This discount rate might be because you care about future people less, or because you expect a d% of pretty much unavoidable existential risk going forward.
Some reference values
N=1010 (10 billion), X=$104, r=0.03 means that willingness to pay for 0.01% risk reduction should be 0.0001∗1010∗$104/0.03=333∗109, i.e., $333 billion
N=7∗109 (7 billion), X=$5∗103, r=0.05 means that willingness to pay for 0.01% risk reduction should be 0.0001∗7∗109∗5∗103/0.05=70∗109 i.e., $70 billion.
I notice that from the perspective of a central world planner, my willingness to pay would be much higher (because my intrinsic discount rate is closer to ~0%). Taking d=0.0001
N=1010 (10 billion), X=$104, r=0.0001 means that willingness to pay for 0.01% risk reduction should be 0.0001∗1010∗$104/0.0001=100∗1012, i.e., $100 trillion
To do:
The above might be the right way to model willingness to pay from 0.02% risk per year to 0.01% risk per year. But with, e.g,. 3% remaining per year, willingness to pay is lower, because over the long-run we all die sooner.
E.g., reducing risk from 0.02% per year to 0.01% per year is much more valuable that reducing risk from 50.1% to 50%.
[1]: Where you value the i-th year in the steady-state at (1−d)i of the value of the first year. If you don’t value future people, the discount rate d might be close to 1, if you do value them, it might be close to 0.
Thinking more about this, these are more of an upper bound, which don’t bind because you can probably buy a 0.01% risk reduction per year much cheaper. So the parameter to estimate would be more like ‘what are the other cheaper interventions’
The steady-state population assumption is my biggest objection here. Everything you’ve written is correct yet I think that one premise is so unrealistic as to render this somewhat unhelpful as a model. (And as always, NPV of the eternal future varies a crazy amount even within a small range of reasonable discount rates, as your numbers show.)
Just to complement Khorton’s answer: With a discount rate of d [1], and a steady-state population of N, and a willingness to pay of $X, the total value of the future is N∗$X/d, so the willingness to pay for 0.01% of it would be 0.01∗N∗$X/d
This discount rate might be because you care about future people less, or because you expect a d% of pretty much unavoidable existential risk going forward.
Some reference values
N=1010 (10 billion), X=$104, r=0.03 means that willingness to pay for 0.01% risk reduction should be 0.0001∗1010∗$104/0.03=333∗109, i.e., $333 billion
N=7∗109 (7 billion), X=$5∗103, r=0.05 means that willingness to pay for 0.01% risk reduction should be 0.0001∗7∗109∗5∗103/0.05=70∗109 i.e., $70 billion.
I notice that from the perspective of a central world planner, my willingness to pay would be much higher (because my intrinsic discount rate is closer to ~0%). Taking d=0.0001
N=1010 (10 billion), X=$104, r=0.0001 means that willingness to pay for 0.01% risk reduction should be 0.0001∗1010∗$104/0.0001=100∗1012, i.e., $100 trillion
To do:
The above might be the right way to model willingness to pay from 0.02% risk per year to 0.01% risk per year. But with, e.g,. 3% remaining per year, willingness to pay is lower, because over the long-run we all die sooner.
E.g., reducing risk from 0.02% per year to 0.01% per year is much more valuable that reducing risk from 50.1% to 50%.
[1]: Where you value the i-th year in the steady-state at (1−d)i of the value of the first year. If you don’t value future people, the discount rate d might be close to 1, if you do value them, it might be close to 0.
Here is a Guesstimate which calculates this in terms of a one-off 0.01% existential risk reduction over a century.
Here is a Guesstimate model which addresses the item on the to-do list. Note that in this guesstimate I’m talking about a −0.01% yearly reduction.
Thinking more about this, these are more of an upper bound, which don’t bind because you can probably buy a 0.01% risk reduction per year much cheaper. So the parameter to estimate would be more like ‘what are the other cheaper interventions’
The steady-state population assumption is my biggest objection here. Everything you’ve written is correct yet I think that one premise is so unrealistic as to render this somewhat unhelpful as a model. (And as always, NPV of the eternal future varies a crazy amount even within a small range of reasonable discount rates, as your numbers show.)
For what it’s worth, I don’t disagree with you, though I do think that the steady state is a lower bound of value, not an upper bound.