So here’s a framing that I found useful, maybe someone else will too.
Given some problem area, let’s say I is the importance of the problem, defined as the total value we gain from solving the whole thing, and write p(r)∈[0,1] for the proportion of the problem solved depending on the total resources r invested (this is the graph in the post).
Now let’s say R is the amount of resources that are currently being used to combat the problem. We want to estimate the current marginal value of additional resources, which is given by I⋅dpdr(R).
The ITN framework splits the second factor into tractability and neglectedness. If we write r′=rR for resources normalized by the current investment R, then
dpdr=dpdr′dr′dr=dpdr′1R.
The factors on the right-hand side represent tractability T=dpdr′ and neglectedness N=1R. So we’ve recovered the familiar I⋅T⋅N = marginal value of additional resources.
But this feels like a kinda clumsy way to do it―it’s not clear what we gain from introducing r′. Instead, we should just try to estimate dpdr(R) directly (this is the main argument I think OP is making).
I think this is on the right track—though as you say its a bit clumsy. There is a similar formalism called the ‘Kaya identity’ (see google—its well known) with the same issues. i’m trying to develop a slightly different and possibly more useful formalism or formula (but i may not succeed)
So here’s a framing that I found useful, maybe someone else will too.
Given some problem area, let’s say I is the importance of the problem, defined as the total value we gain from solving the whole thing, and write p(r)∈[0,1] for the proportion of the problem solved depending on the total resources r invested (this is the graph in the post).
Now let’s say R is the amount of resources that are currently being used to combat the problem. We want to estimate the current marginal value of additional resources, which is given by I⋅dpdr(R).
The ITN framework splits the second factor into tractability and neglectedness. If we write r′=rR for resources normalized by the current investment R, then
The factors on the right-hand side represent tractability T=dpdr′ and neglectedness N=1R. So we’ve recovered the familiar I⋅T⋅N = marginal value of additional resources.
But this feels like a kinda clumsy way to do it―it’s not clear what we gain from introducing r′. Instead, we should just try to estimate dpdr(R) directly (this is the main argument I think OP is making).
I think this is on the right track—though as you say its a bit clumsy. There is a similar formalism called the ‘Kaya identity’ (see google—its well known) with the same issues. i’m trying to develop a slightly different and possibly more useful formalism or formula (but i may not succeed)