Here is that review I mentioned. I’ll try and add this post to that summary when I get a chance, though I can’t do justice to all the mathematical details.
If you do give it a glance, I’d be curious to hear your thoughts on the critiques regarding the shape and size of the marginal returns graph. It’s these concerns that I found most compelling as fundamental critiques of using ITN as more than a rough first-pass heuristic.
I’ve added a summary at the start of the Bonus section you could use:
When there’s uncertainty in the factors and they correlate positively, we may be underestimating the marginal cost-effectiveness. When there’s uncertainty in the factors and they correlate negatively, we may be overestimating the marginal cost-effectiveness.
(And this is because we’re taking the product of the expected values rather than the expected value of the product and not explicitly modelling correlations between terms.)
Is this about Neglectedness assuming diminishing marginal returns? I think if you try to model the factors as they’re defined formally and mathematically by 80,000 Hours, Tractability can capture effects in the opposite direction and, e.g. increasing marginal returns. At any rate, if the terms, as defined mathematically, are modelled properly (and assuming no division by zero issues), then when we take the product, we get Good done / extra resources, and there’s nothing there that implies an assumption of diminishing or increasing marginal returns, so if Neglectedness assumes diminishing marginal returns, then the other factors assume increasing marginal returns to compensate.
How many extra resources we consider in Neglectedness could be important, though, and it could be the case that Good done / extra resources is higher or lower depending on the size of “extra resources”. I think this is where we would see diminishing or increasing marginal returns, but no assumption either way.