The end of this post will be beyond my math til next year, so I’m glad you wrote it :)
Have you given thought to the pre-existing critiques of the ITN framework? I’ll link to my review of them later.
I think I’ve looked at a few briefly.
I think the framework is mostly fine theoretically, based on the formal definitions of the (linear scale) terms and their product as a cost-effectiveness estimate. I’d imagine the concerns are more with the actual interpretation and application. For example, Neglectedness is calculated based on current resouces, not also projected resources, so an issue might not be really neglected, because you expect resources to increase in the future without your intervention. This accounts partially for “urgency”.
Can you give an example of how an EA organization presently using ITN could improve their analysis by implementing some of the changes and considerations you’re pointing out?
I think EA orgs are mostly not making the mistakes I describe in each of sections 1, 2 and 3, but the solution is pretty straightforward: consider the possibility of negative outcomes, and take expectations before taking logarithms.
For the Bonus section, my suggestion would be to give (independent) distributions for each of the factors, and check the bounds I describe in “Bounding the error.” to check how sensitive the analysis could be to dependencies, and if it’s not sensitive enough to change your priorities, then proceed as usual. If you find that it could be sensitive enough and you think there may be dependencies, model dependencies in the distributions and actually calculate/estimate the expected value of the product (using Guesstimate, for example, but keeping in mind that extremely unlikely outcomes might not get sampled, so if most of the value is in those, your estimate will usually be way off).
Or you can just rely on cost-effectiveness analyses for specific interventions when they’re available, but they aren’t always available.
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.