From my experience last year writing the post you linked to (which I now just edited), I would really dumb things down and try to make the graphical example as simple as possible for people with ~high-school math knowledge (like me)
Several smart people I asked for advice about that post seemed to find reasoning about this not trivial, gave somewhat contradicting answers, or thought that the solution I had thought of was too obvious to post, despite it being very wrong (as you explained in the comments last year, thank you!) Even after a year, tbh I’m not sure I “grok” it completely (see the appendix I added to the post. But I reassure myself with the fact that costs very rarely span across orders of magnitude, and in those cases, I could try to model E(value) directly rather than E(value/cost) as a proxy).
Things to add:
Graphical example
Explicit discussion of GiveWell’s use of cost/effect
Real-world examples where this causes a significant error
Expand on the lognormal example, discuss cases where the variance is in the same order of magnitude as the expected value
What this says about how we should model uncertainty
From my experience last year writing the post you linked to (which I now just edited), I would really dumb things down and try to make the graphical example as simple as possible for people with ~high-school math knowledge (like me)
Several smart people I asked for advice about that post seemed to find reasoning about this not trivial, gave somewhat contradicting answers, or thought that the solution I had thought of was too obvious to post, despite it being very wrong (as you explained in the comments last year, thank you!) Even after a year, tbh I’m not sure I “grok” it completely (see the appendix I added to the post. But I reassure myself with the fact that costs very rarely span across orders of magnitude, and in those cases, I could try to model E(value) directly rather than E(value/cost) as a proxy).
Thanks! Yeah, I totally agree—the topic is surprisingly delicate and nonintuitive, and my examples above are too technical.
By the way, I’d love it if other people would write posts that make the exact same point but better! (or for different audiences).