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.
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.)
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’
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 model which addresses the item on the to-do list. Note that in this guesstimate I’m talking about a −0.01% yearly reduction.
Here is a Guesstimate which calculates this in terms of a one-off 0.01% existential risk reduction over a century.
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.
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’