I was wondering why you didn't take the geometric mean, as Guy mentioned upthread -- intuitively you'd expect the *log* of country population to be evenly distributed, since assuming the (non-log-transformed) country pops to be evenly distributed doesn't make much sense when the endpoints are a rounding error away from zero on one end and China on the other. You would've basically nailed this Fermi exercise. Of course that's not a straightforwardly generalizable takeaway though.
But there is a generalizable takeaway from this ostensible nitpick (I think), which is to familiarize yourself with lots of real-world examples of distributions. The "strategy" here is mainly broad reading plus doing frequent little Fermi estimates from time to time.
It's by a Good Judgment superforecaster, Nuno Sempere. I thought it was a cool look into how a world-class estimation guy does his thing, even if his methods are way too effortful for me.
How to pick a number for any purpose
I was wondering why you didn't take the geometric mean, as Guy mentioned upthread -- intuitively you'd expect the *log* of country population to be evenly distributed, since assuming the (non-log-transformed) country pops to be evenly distributed doesn't make much sense when the endpoints are a rounding error away from zero on one end and China on the other. You would've basically nailed this Fermi exercise. Of course that's not a straightforwardly generalizable takeaway though.
But there is a generalizable takeaway from this ostensible nitpick (I think), which is to familiarize yourself with lots of real-world examples of distributions. The "strategy" here is mainly broad reading plus doing frequent little Fermi estimates from time to time.
Just to not sound like a party-pooper I'd like to balance out my comment by saying I enjoyed your post, and I'd like to share a related article: https://forum.effectivealtruism.org/posts/3hH9NRqzGam65mgPG/five-steps-for-quantifying-speculative-interventions
It's by a Good Judgment superforecaster, Nuno Sempere. I thought it was a cool look into how a world-class estimation guy does his thing, even if his methods are way too effortful for me.
I will usually take the geometric mean when estimating magnitudes like this.
[100K, 15M] ==> 1.2M
[3M, 25M] ==> 8.6M