Edit: My comment is wrong—i had misread the price as £1 billion as a one-off, but it is £1 billion per year
I’m not quite able to follow what role annualising the risk plays in your model, since as far as I can tell you seem to calculate your final cost effectiveness in terms purely of the risk reduction in 1 year. This seems like it should undercount the impact 100-fold.
e.g. if I skip annualising entirely, and just work in century blocks I get:
still 247 Billion Life years at stake
1% chance of x-risk, reduced to 0.99% by £1 billion project X.
This expected £ per year of life at 10^9/0.01%*247*10^9 = ~40, which is about 1⁄100 of your answer.
I might well have misunderstood some important part of your model, or be making some probability-related mistake.
The mistake might be on my part, but I think where this may be going wrong is I assume the cost needs to be repeated each year (i.e. you spent 1B to reduce risk by 1% in 2018, then have to spend another 1B to reduce risk by 1% in 2019). So if you assume a single 1B pulse reduces x risk across the century by 1%, then you do get 100 fold better results.
I mainly chose the device of some costly ‘project X’ as it is hard to get a handle on (e.g.) whether 10^-10 reduction in xrisk/$ is a plausible figure or not. Given this, I might see if I can tweak the wording to make it clearer—or at least make any mistake I am making easier to diagnose.
Edit: My comment is wrong—i had misread the price as £1 billion as a one-off, but it is £1 billion per year
I’m not quite able to follow what role annualising the risk plays in your model, since as far as I can tell you seem to calculate your final cost effectiveness in terms purely of the risk reduction in 1 year. This seems like it should undercount the impact 100-fold.
e.g. if I skip annualising entirely, and just work in century blocks I get:
still 247 Billion Life years at stake
1% chance of x-risk, reduced to 0.99% by £1 billion project X.
This expected £ per year of life at 10^9/0.01%*247*10^9 = ~40, which is about 1⁄100 of your answer.
I might well have misunderstood some important part of your model, or be making some probability-related mistake.
The mistake might be on my part, but I think where this may be going wrong is I assume the cost needs to be repeated each year (i.e. you spent 1B to reduce risk by 1% in 2018, then have to spend another 1B to reduce risk by 1% in 2019). So if you assume a single 1B pulse reduces x risk across the century by 1%, then you do get 100 fold better results.
I mainly chose the device of some costly ‘project X’ as it is hard to get a handle on (e.g.) whether 10^-10 reduction in xrisk/$ is a plausible figure or not. Given this, I might see if I can tweak the wording to make it clearer—or at least make any mistake I am making easier to diagnose.
Ah sorry yes you are right—I had misread the cost as £1 Billion total, not £1 Billion per year!