Iām confused by some of the set-up here. When considering catastrophes, your ācost to save a lifeā represents the cost to save that life conditional on the catastrophe being due to occur? (Iām not saying āconditional on occurringā because presumably youāre allowed interventions which try to avert the catastrophe.)
My language was confusing. By āpre- and post-catastrophe populationā, 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 youāre 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 isnāt speaking to my central question. Iāll try asking via an example:
Suppose we think that thereās 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) donāt condition on C, so you save an expected 0.01% of people at a cost of $Y?
Iād naively have expected you to do B) (from the natural language descriptions), but when I look at your calculations it seems like youāve 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)ĻµB).
The PDF of the ratio between the initial and final population (f=Ī±(Pi/Pf)ā(Ī±+1)), which is meant to reflect the probability of a catastrophe.
Iām worried Iām misunderstanding what you mean by āvalue densityā. Could you perhaps spell this out with a stylized example, e.g. comparing two different interventions protecting against different sizes of catastrophe?
By āpre- and post-catastrophe populationā, 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 āperiod of 1 yearā to āany period of 1 year (e.g. a calendar year)ā. Population has been growing, so my ratio between the initial and final population will have a high chance of being lower than 1.
My language was confusing. By āpre- and post-catastrophe populationā, 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 isnāt speaking to my central question. Iāll try asking via an example:
Suppose we think that thereās 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) donāt condition on C, so you save an expected 0.01% of people at a cost of $Y?
Iād naively have expected you to do B) (from the natural language descriptions), but when I look at your calculations it seems like youāve 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)ĻµB).
The PDF of the ratio between the initial and final population (f=Ī±(Pi/Pf)ā(Ī±+1)), which is meant to reflect the probability of a catastrophe.
Iām worried Iām misunderstanding what you mean by āvalue densityā. 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 āperiod of 1 yearā to āany period of 1 year (e.g. a calendar year)ā. Population has been growing, so my ratio between the initial and final population will have a high chance of being lower than 1.