Also, to be clear, this is supposed to be ~immediately pre-catastrophe and ~immediately post-catastrophe, right? (Catastrophes can probably take time, but presumably we can still define pre- and post-catastrophe periods.)
I have updated the post changing āpre- and post-catastrophe populationā to āpopulation at the start and end of a period of 1 yearā, which I now also refer to as the initial and final population.
Youāre modelling the cost-effectiveness of saving a life conditional on catastrophe here, right?
No. It is supposed to be the cost-effectiveness as a function of the ratio between the initial and final population.
Typically x-risk interventions aim at reducing the risk of catastrophe, not the benefits conditional on catastrophe.
Yes, interpreting catastrophe as a large population loss. In my framework, xrisk interventions aim to save lives over periods whose initial population is significantly higher than the final one.
Oh, I didnāt mean for you to define the period explicitly as a fixed interval period. I assume this can vary by catastrophe. Like maybe population declines over 5 years with massive crop failures. Or, an engineered pathogen causes massive population decline in a few months.
I just wasnāt sure what exactly you meant. Another intepretation would be that P_f is the total post-catastrophe population, summing over all future generations, and I just wanted to check that you meant the population at a given time, not aggregating over time.
Oh, I didnāt mean for you to define the period explicitly as a fixed interval period. I assume this can vary by catastrophe. Like maybe population declines over 5 years with massive crop failures. Or, an engineered pathogen causes massive population decline in a few months.
Hi @MichaelStJules, I am tagging you because I have updated the following sentence. If there is a period longer than 1 year over which population decreases, the power laws describing the ratio between the initial and final population of each of the years following the 1st could have different tail indices, with lower tail indices for years in which there is a larger population loss. I do not think the duration of the period is too relevant for my overall point. For short and long catastrophes, I expect the PDF of the ratio between the initial and final population to decay faster than the benefits of saving a life, such that the expected value density of the cost-effectiveness decreases with the severity of the catastrophe (at least for my assumption that the cost to save a life does not depend on the severity of the catastrophe).
I just wasnāt sure what exactly you meant. Another intepretation would be that P_f is the total post-catastrophe population, summing over all future generations, and I just wanted to check that you meant the population at a given time, not aggregating over time.
I see! Yes, both Pi and Pf are population sizes at a given point in time.
Thanks for the comment, Michael!
I have updated the post changing āpre- and post-catastrophe populationā to āpopulation at the start and end of a period of 1 yearā, which I now also refer to as the initial and final population.
No. It is supposed to be the cost-effectiveness as a function of the ratio between the initial and final population.
Yes, interpreting catastrophe as a large population loss. In my framework, xrisk interventions aim to save lives over periods whose initial population is significantly higher than the final one.
Oh, I didnāt mean for you to define the period explicitly as a fixed interval period. I assume this can vary by catastrophe. Like maybe population declines over 5 years with massive crop failures. Or, an engineered pathogen causes massive population decline in a few months.
I just wasnāt sure what exactly you meant. Another intepretation would be that P_f is the total post-catastrophe population, summing over all future generations, and I just wanted to check that you meant the population at a given time, not aggregating over time.
Hi @MichaelStJules, I am tagging you because I have updated the following sentence. If there is a period longer than 1 year over which population decreases, the power laws describing the ratio between the initial and final population of each of the years following the 1st could have different tail indices, with lower tail indices for years in which there is a larger population loss. I do not think the duration of the period is too relevant for my overall point. For short and long catastrophes, I expect the PDF of the ratio between the initial and final population to decay faster than the benefits of saving a life, such that the expected value density of the cost-effectiveness decreases with the severity of the catastrophe (at least for my assumption that the cost to save a life does not depend on the severity of the catastrophe).
I see! Yes, both Pi and Pf are population sizes at a given point in time.