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.
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.