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.
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.