What we ultimately care about is marginal utility per dollar, MU/$ (or marginal cost-effectiveness). ITN is a way of proxying MU/$ when we can’t easily estimate it directly.
Definitions:
Importance = utility gained from solving the entire problem.
Tractability = percent of problem solved per dollar.
Neglectedness = amount of resources allocated to the problem.
Note that tractability can be a function of neglectedness: the amount of the problem solved per dollar will likely vary depending on how many resources are already allocated. This is to capture diminishing returns, as we expect the first dollar spent on a problem to be more effective in solving it than the millionth dollar.
Then to get MU/$ as a function of neglectedness, we multiply importance and tractability:
MU/$ = utility(total problem) * % solved/$ (=f(resources)). Now we have MU/$ as a function of resources, so to figure out where we are on the MU/$ curve, we plug in the value of resources (neglectedness).
Here’s an example without diminishing returns: suppose solving an entire problem increases utility by 100 utils, so importance = 100 utils. And suppose tractability is 1% of the problem solved per dollar. Note that this doesn’t vary with resources spent, so there aren’t diminishing returns. Then MU/$ = 100 utils * 0.01/$ = 1 util/$. Here, neglectedness (defined as resources spent) doesn’t matter, except when spending hits $100 and the problem is fully solved.
Now let’s introduce diminishing returns. Let’s denote resources spent by x. As before, importance = 100 utils. But now, suppose tractability is (1/x)% of the problem solved per dollar. Now we have diminishing returns: the first dollar solves 1% of the problem, but the tenth dollar solves 0.1%. Here MU/$ = 100 utils * (1/x)%/$ = 1/x utils/$. To evaluate the MU/$ of this problem, we need to know how neglected it is, captured by how many resources, x, have already been spent.
Hence, importance and tractability define MU/$ as a function of neglectedness, and neglectedness determines the specific value of MU/$.
This is how I think about the ITN framework:
What we ultimately care about is marginal utility per dollar, MU/$ (or marginal cost-effectiveness). ITN is a way of proxying MU/$ when we can’t easily estimate it directly.
Definitions:
Importance = utility gained from solving the entire problem.
Tractability = percent of problem solved per dollar.
Neglectedness = amount of resources allocated to the problem.
Note that tractability can be a function of neglectedness: the amount of the problem solved per dollar will likely vary depending on how many resources are already allocated. This is to capture diminishing returns, as we expect the first dollar spent on a problem to be more effective in solving it than the millionth dollar.
Then to get MU/$ as a function of neglectedness, we multiply importance and tractability: MU/$ = utility(total problem) * % solved/$ (=f(resources)). Now we have MU/$ as a function of resources, so to figure out where we are on the MU/$ curve, we plug in the value of resources (neglectedness).
Here’s an example without diminishing returns: suppose solving an entire problem increases utility by 100 utils, so importance = 100 utils. And suppose tractability is 1% of the problem solved per dollar. Note that this doesn’t vary with resources spent, so there aren’t diminishing returns. Then MU/$ = 100 utils * 0.01/$ = 1 util/$. Here, neglectedness (defined as resources spent) doesn’t matter, except when spending hits $100 and the problem is fully solved.
Now let’s introduce diminishing returns. Let’s denote resources spent by x. As before, importance = 100 utils. But now, suppose tractability is (1/x)% of the problem solved per dollar. Now we have diminishing returns: the first dollar solves 1% of the problem, but the tenth dollar solves 0.1%. Here MU/$ = 100 utils * (1/x)%/$ = 1/x utils/$. To evaluate the MU/$ of this problem, we need to know how neglected it is, captured by how many resources, x, have already been spent.
Hence, importance and tractability define MU/$ as a function of neglectedness, and neglectedness determines the specific value of MU/$.