Thanks for the detailed response, Vasco! Apologies in advance that this reply is slightly rushed and scattershot.
I agree that you are right with the maths—it is 251x, not 63,000x.
I am not comparing the cost-effectiveness of preventing events of different magnitudes.
Instead, I am comparing the cost-effectiveness of saving lives in periods of different population losses.
OK, I did not really get this!
In your example on wars you say
As a consequence, if the goal is minimising war deaths[2], spending to save lives in wars 1 k times as deadly should be 0.00158 % (= (10^3)^(-1.6)) as large.
Can you give an example of what might count as “spending to save lives in wars 1k times as deadly” in this context?
I am guessing it is spending money now on things that would save lives in very deadly wars. Something like building a nuclear bunker vs making a bullet proof vest? Thinking about the amounts we might be willing to spend on interventions that save lives in 100-death wars vs 100k-death wars, it intuitively feels like 251x is a way better multiplier than 63,000. So where am I going wrong?
When you are thinking about the PDF of PiPf, are you forgetting that ∇PiPf is not proportional to ∇Pf?
To give a toy example: suppose Pi=100.
Then if 90<pf<100 we have 1<PiPf<1.11
If 10<pf<20 we have 5<PiPf<10
The “height of the PDF graph” will not capture these differences in width. This won’t matter much for questions of 100 vs 100k deaths, but it might be relevant for near-existential mortality levels.
Can you give an example of what might count as “spending to save lives in wars 1k times as deadly” in this context?
For example, if one was comparing wars involding 10 k or 10 M deaths, the latter would be more likely to involve multiple great power, in which case it would make more sense to improve relationships between NATO, China and Russia.
Thinking about the amounts we might be willing to spend on interventions that save lives in 100-death wars vs 100k-death wars, it intuitively feels like 251x is a way better multiplier than 63,000. So where am I going wrong?
You may be right! Interventions to decrease war deaths may be better conceptualised as preventing deaths within a given severity range, in which case I should not have interpreted lirerally the example in Founders Pledge’s report Philanthropy to the Right of Boom. In general, I think one has to rely on cost-effectiveness analyses to decide what to prioritise.
When you are thinking about the PDF of PiPf, are you forgetting that ∇PiPf is not proportional to ∇Pf?
I am not sure I got the question. In my discussion of Founders Pledge’s example about war deaths, I assumed the value of saving one life to be the same regardless of population size, because this is what they were doing). So I did not use the ratio between the initial and population.
Thanks for the detailed response, Vasco! Apologies in advance that this reply is slightly rushed and scattershot.
I agree that you are right with the maths—it is 251x, not 63,000x.
OK, I did not really get this!
In your example on wars you say
Can you give an example of what might count as “spending to save lives in wars 1k times as deadly” in this context?
I am guessing it is spending money now on things that would save lives in very deadly wars. Something like building a nuclear bunker vs making a bullet proof vest? Thinking about the amounts we might be willing to spend on interventions that save lives in 100-death wars vs 100k-death wars, it intuitively feels like 251x is a way better multiplier than 63,000. So where am I going wrong?
When you are thinking about the PDF of PiPf, are you forgetting that ∇PiPf is not proportional to ∇Pf?
To give a toy example: suppose Pi=100.
Then if 90<pf<100 we have 1<PiPf<1.11
If 10<pf<20 we have 5<PiPf<10
The “height of the PDF graph” will not capture these differences in width. This won’t matter much for questions of 100 vs 100k deaths, but it might be relevant for near-existential mortality levels.
For example, if one was comparing wars involding 10 k or 10 M deaths, the latter would be more likely to involve multiple great power, in which case it would make more sense to improve relationships between NATO, China and Russia.
You may be right! Interventions to decrease war deaths may be better conceptualised as preventing deaths within a given severity range, in which case I should not have interpreted lirerally the example in Founders Pledge’s report Philanthropy to the Right of Boom. In general, I think one has to rely on cost-effectiveness analyses to decide what to prioritise.
I am not sure I got the question. In my discussion of Founders Pledge’s example about war deaths, I assumed the value of saving one life to be the same regardless of population size, because this is what they were doing). So I did not use the ratio between the initial and population.