I’m confused by some of the set-up here. When considering catastrophes, your “cost to save a life” represents the cost to save that life conditional on the catastrophe being due to occur? (I’m not saying “conditional on occurring” because presumably you’re allowed interventions which try to avert the catastrophe.)
Understood this way, I find this assumption very questionable:
ϵC=0, since I feel like the effect of having more opportunities to save lives in catastrophes is roughly offset by the greater difficulty of preparing to take advantage of those opportunities pre-catastrophe.
Or is the point that you’re only talking about saving lives via resilience mechanisms in catastrophes, rather than trying to make the catastrophes not happen or be small? But in that case the conclusions about existential risk mitigation would seem unwarranted.
I’m confused by some of the set-up here. When considering catastrophes, your “cost to save a life” represents the cost to save that life conditional on the catastrophe being due to occur? (I’m not saying “conditional on occurring” because presumably you’re allowed interventions which try to avert the catastrophe.)
My language was confusing. By “pre- and post-catastrophe population”, I meant the population at the start and end of a period of 1 year, which I now also refer to as the initial and final population. I have now clarified this in the post.
I assume the cost to save a life in a given period is a function of the ratio between the initial and final population of the period.
Or is the point that you’re only talking about saving lives via resilience mechanisms in catastrophes, rather than trying to make the catastrophes not happen or be small? But in that case the conclusions about existential risk mitigation would seem unwarranted.
I meant to refer to all mechanisms (e.g. prevention, response and resilience) which affect the variation in population over a period.
Sorry, this isn’t speaking to my central question. I’ll try asking via an example:
Suppose we think that there’s a 1% risk of a particular catastrophe C in a given time period T which kills 90% of people
We can today make an intervention X, which costs $Y, and means that if C occurs then T will only kill 89% of people
We pay the cost $Y in all worlds, including the 99% in which C never occurs
When calculating the cost to save a life for X, do you:
A) condition on C, so you save 1% of people at the cost of $Y; or
B) don’t condition on C, so you save an expected 0.01% of people at a cost of $Y?
I’d naively have expected you to do B) (from the natural language descriptions), but when I look at your calculations it seems like you’ve done A). Is that right?
Thanks for clarifying! I agree B) makes sense, and I am supposed to be doing B) in my post. I calculated the expected value density of the cost-effectiveness of saving a life from the product between:
A factor describing the value of saving a life (B=kB(Pi/Pf)ϵB).
The PDF of the ratio between the initial and final population (f=α(Pi/Pf)−(α+1)), which is meant to reflect the probability of a catastrophe.
I’m worried I’m misunderstanding what you mean by “value density”. Could you perhaps spell this out with a stylized example, e.g. comparing two different interventions protecting against different sizes of catastrophe?
By “pre- and post-catastrophe population”, I meant the population at the start and end of a period of 1 year, which I now also refer to as the initial and final population.
I guess you are thinking that the period of 1 year I mention above is one over which there is a catastrophe, i.e. a large reduction in population. However, I meant a random unconditioned year. I have now updated “period of 1 year” to “any period of 1 year (e.g. a calendar year)”. Population has been growing, so my ratio between the initial and final population will have a high chance of being lower than 1.
I’m confused by some of the set-up here. When considering catastrophes, your “cost to save a life” represents the cost to save that life conditional on the catastrophe being due to occur? (I’m not saying “conditional on occurring” because presumably you’re allowed interventions which try to avert the catastrophe.)
Understood this way, I find this assumption very questionable:
Or is the point that you’re only talking about saving lives via resilience mechanisms in catastrophes, rather than trying to make the catastrophes not happen or be small? But in that case the conclusions about existential risk mitigation would seem unwarranted.
My language was confusing. By “pre- and post-catastrophe population”, I meant the population at the start and end of a period of 1 year, which I now also refer to as the initial and final population. I have now clarified this in the post.
I assume the cost to save a life in a given period is a function of the ratio between the initial and final population of the period.
I meant to refer to all mechanisms (e.g. prevention, response and resilience) which affect the variation in population over a period.
Sorry, this isn’t speaking to my central question. I’ll try asking via an example:
Suppose we think that there’s a 1% risk of a particular catastrophe C in a given time period T which kills 90% of people
We can today make an intervention X, which costs $Y, and means that if C occurs then T will only kill 89% of people
We pay the cost $Y in all worlds, including the 99% in which C never occurs
When calculating the cost to save a life for X, do you:
A) condition on C, so you save 1% of people at the cost of $Y; or
B) don’t condition on C, so you save an expected 0.01% of people at a cost of $Y?
I’d naively have expected you to do B) (from the natural language descriptions), but when I look at your calculations it seems like you’ve done A). Is that right?
Thanks for clarifying! I agree B) makes sense, and I am supposed to be doing B) in my post. I calculated the expected value density of the cost-effectiveness of saving a life from the product between:
A factor describing the value of saving a life (B=kB(Pi/Pf)ϵB).
The PDF of the ratio between the initial and final population (f=α(Pi/Pf)−(α+1)), which is meant to reflect the probability of a catastrophe.
I’m worried I’m misunderstanding what you mean by “value density”. Could you perhaps spell this out with a stylized example, e.g. comparing two different interventions protecting against different sizes of catastrophe?
I guess you are thinking that the period of 1 year I mention above is one over which there is a catastrophe, i.e. a large reduction in population. However, I meant a random unconditioned year. I have now updated “period of 1 year” to “any period of 1 year (e.g. a calendar year)”. Population has been growing, so my ratio between the initial and final population will have a high chance of being lower than 1.