Hmm, I’m not sure Iunderstand your point so maybe let me add some more numbers to what I’m saying and you could say if you think your point is responsive?
What I think you’re saying is that I’m estimating E[value saving one life / value stopping extinction] rather than E[value of saving one life] / E[value of stopping extinction]. I think this is wrong and that I’m doing the latter.
I start from the premise of we want to save in expectation most lives (current and future are equivalent). Let’s say I have two options…I can prevent extinction or directly stop a random living person from dying. Assume there are 10^35 (I just want N >> C) future lives and there are 10^10 current lives. Now assume I believe there is a 99% chance that when I save this one life, fertility in the future somehow goes up such that the individual’s progeny are replaced, but there’s a 1% chance the individual’s progeny is not replaced. The individual is responsible for 10^35/10^10 =10^25 progeny. This gives E[stopping random living person from dying] ~ 1%*10^25 =10^23.
And we’d agree E[preventing extinction] = 10^35. So E[value of saving one life] / E[value of stopping extinction] ~ 10^-12.
Interestingly E[value of saving one life / value of stopping extinction] is the same in this case because the denominator is just a constant random variable…though E[value of stopping extinction/value of saving one life] is very very large (much larger than 10^12).
Edit: I misread and thought you were saying non-Malthusian worlds had more lives at first; realized you said the opposite, so we’re saying the same thing and we agree. Will have to do more math about this.
This is an interesting point that I hadn’t considered! I think you’re right that non-Malthusian futures are much larger than Malthusian futures in some cases...though if i.e. the “Malthusian” constraint is digital lives or such, not sure.
I think the argument you make actually cuts the other way. That to go back to the expected value...the case where the single death is deriving its EV from is precisely the non-Malthusian scenarios (when its progeny is not replaced by future progeny) so its EV actually remains the same. The extinction EV is the one that reduces...so you’ll actually get a number much less than 10^10 if you have high credence that Malthusianism is true and think Malthusian worlds have more people.
But, if you believe the opposite...that Malthusian worlds have more people, which I have not thought about but actually think might be true, yes a bigger gap than 10^10; will have to think about this.
Thanks! Does this make sense to you?