Formalizing the cause prioritization framework

When prioritizing causes, what we ultimately care about is how much good we can do per unit of resources. In formal terms, we want to find the causes with the highest marginal utility per dollar, $MU/\$$ (or, marginal cost-effectiveness). The Importance-Tractability-Neglectedness (ITN) framework has been used as a way of calculating $MU/\$$ by estimating its component parts. In this post I...

(see also recent posts by John Halstead and Michael Plant).

80k defines ITN as follows:

• Importance = utility gained / % of problem solved
• Tractability = % of problem solved / % increase in resources
• Neglectedness = % increase in resources / extra $

With these definitions, multiplying all three factors gives us utility gained / extra $, or MU/$ (as the middle terms cancel out). However, I will make two small amendments to this setup. First, it seems artificial to have a term for "% increase in resources", since what we care about is the per-dollar effect of our actions. Hence, we can instead define tractability as "% of problem solved / extra $", and eliminate the third factor from the main definition. So to calculate MU/$, we simply multiply importance and tractability:

$MU/\$=$ $\frac{\text{utility gained}}{\%\text{of problem solved}}$ $\times$ $\frac{\%\text{of problem solved}}{\text{extra}\$}$

This defines MU/$ as a function of the amount of resources allocated to a problem, which brings me to my second amendment. Apart from the above definition, 80k defines 'neglectedness' informally as the amount of resources allocated to solving a problem. This definition is confusing, because the everyday meaning of 'neglected' is "improperly ignored". To say that a cause is neglected intuitively means that it is ignored relative to its cost-effectiveness. But if neglectedness is supposed to be a proxy for cost-effectiveness, this everyday meaning is circular. And really, how useful is the advice to focus on causes that have been improperly ignored?

I suggest we instead use "crowdedness" to mean the amount of resources allocated to a problem. This captures intuitions about diminishing returns (other things equal, a more crowded cause is less cost-effective), and avoids the problem of having a relative standard as the everyday meaning.

Thus, our revised framework is now ITC:

• Importance = utility gained / % of problem solved
• Tractability = % of problem solved / $
• Crowdedness = $ allocated to the problem

So how does crowdedness fit into this setup? Intuitively, tractability will be a function of crowdedness: the % of the problem solved per dollar will vary depending on how many resources are already allocated. This is the phenomenon of diminishing marginal returns, where the first dollar spent on a problem is more effective in solving it than is the millionth dollar. Hence, crowdedness tells us where we are on the tractability function.

Let's see how this works graphically. First, we start with tractability as a function of crowdedness. With diminishing marginal returns, "% solved/$" is decreasing in resources.

(Fig 1)

Next, we multiply tractability by importance to obtain MU/$ as a function of resources. Since we assumed "utility gained/% solved" is a constant function, all this does is change the units on the y-axis.

(Fig 2)

Now we can clearly see the amount of good done for an additional dollar, for every level of resources invested. To decide whether we should invest more in a cause, we calculate the current level of resources invested, then evaluate the MU/$ function at that level of resources. We do this for all causes, and allocate resources first to the highest MU/$ causes, and ultimately equalizing MU/$ across all causes.

While MU/$ is sufficient for prioritizing across causes, we can also look at total utility, by integrating the MU/$ function over resources spent. Figure 3 plots the total utility gained from spending on a problem, as a function of resources spent. Note that the slope is equal to MU/$, which is decreasing in $.

(Fig 3)

To compare two causes against each other, we plot their MU/$ functions on the same graph, and compare their MU/$ evaluated at their current level of resources. To maximize utility, we allocate our next dollar to the cause with the highest value of MU/$.

Note that all three factors in the ITC framework are necessary to draw a conclusion about which cause is best.

• (does 80k technique of multiplying/adding logs make any sense?)

[M]ass immunisation of children is an extremely effective intervention to improve global health, but it is already being vigorously pursued by governments and several major foundations, including the Gates Foundation. This makes it less likely to be a top opportunity for future donors.

This last sentence is not strictly true. To be precise, all we can say is that other things equal, a cause with more resources has lower MU/$. That is, for two causes with the same MU/$ function, the cause with higher resources will be farther along the function, and hence have a lower MU/$. If other things are not equal, the cause with more resources may have higher or lower MU/$.

Comparative statics

[goal is showing counterexamples: a cause with low tractability can be high mu/$]

[throw this in appendix, just show one in text?]

In this framework, importance can outweigh tractability, and vice versa; importance and tractability can each outweigh crowdedness; however, crowdedness cannot outweigh importance or tractability.[fn2] Let's show this graphically.

Tractability(C1) < Tractability(C2)

First, let's consider the case where cause C1 is less tractable than cause C2. There are two sub-cases, holding importance and crowdedness constant. First, Fig.5 holds importance constant. As before, this means that the tractability and MU functions have the same shape, and only the y-axis units change.

[fig 5]

Since cause1 is less tractable than cause2 at every value of $, and they have the same importance, the MU/$ of cause1 is higher than the MU/$ of cause2 for every value of $. Hence, if a cause is less tractable than another, holding importance constant, it cannot have higher MU/$, regardless of its crowdedness.[fn3]

Next, we hold crowdedness constant in Fig 6, but allow C1 to be more important than C2. Multiplying importance and tractability flips the ordering. Despite being less tractable, C1's importance gives it a higher MU/$, for a fixed $.

[fig6]

Importance(C1) < Importance(C2)

Second, let's suppose that C1 is less important than C2. Again, there are two sub-cases. First, Fig.7 holds tractability constant, so C1 and C2 have the same tractability function. But since C1 has lower importance, MU/$ of C1 is lower for all values of $. That is, regardless of crowdedness, C2 is always better than C1.

[fig7]

Next, let's hold crowdedness constant in Fig.8, but allow C1 to be more tractable than C2. Here, multiplying importance and tractability reduces the gap between C1 and C2, but C1 still has higher MU/$ at a fixed $. Hence, high tractability can outweigh low importance, holding crowdedness constant.

[fig8]

Crowdedness(C1)>Crowdedness(C2)

Third, assume C1 is more crowded than C2. Let's start by holding importance constant, but allow C1 to be more tractable. Then despite C1 being more crowded, its higher tractability translates into a higher MU/$.

[Fig9]

Finally, hold tractability constant, but allow C1 to be more important. Here again, C1's crowdedness is outweighed by it's importance.

[fig10]

Hence, when other things are not equal, more crowded causes can be higher MU/$.

[make a table, summarizing results?]

[But 80k framework implies that a high C score can outweigh both I and T. This is impossible in my version. Could be due to definition of C as "% increase in resources/$" and T as "% solved /% increase in resources"?]

Implications

One implication of this setup is that we can clearly see how $MU/\$$ depends on the context (in particular, resources spent). For example, AI risk might have had the highest $MU/\$$ in 2013, but the funding boost from OpenAI pushed it to a lower value of $MU/\$$. Hence, claims about "cause C is the highest priority" should be framed as "cause C is the highest priority, given current funding levels". We should expect the "best" cause (defined as highest MU/$) to change over time as spending changes, which we could indicate by using a time subscript, $MU/{\$}_t$.

Note that this model also incorporates Joey Savoie's argument about using the limiting factor instead of importance. Here, a limiting factor would show up as strongly diminishing returns in the tractability function at some level of spending. That is, the percent of the problem solved per dollar would drop off sharply after spending some level of resources on the problem.

We can answer Michael Plant's question about whether it makes sense to distinguish between cause prioritization and intervention evaluation.

Footnotes

[1] We can think of "utility gained / % of problem solved" as a nonlinear function of "% of problem solved". For example, we get 100utils from solving the 1st percent of a problem, but only 10utils from solving the 50th percent. I'm not sure, but it seems better to instead define importance as a scalar, so that "utility gained / % of problem solved" is a constant function of "% of problem solved". That is, solving 1% of the problem just means gaining 1% of the total utility from solving the problem.

[2] This is in contrast to the 80k model, where points are allocated to each of the three factors, and then summed to create a single cost-effectiveness score for each cause. On their model, a cause with scores of {I=0, T=0, C=12} would be more cost-effective than a cause with scores of {I=4, T=4, C=2}, since 0+0+12=12 > 10 = 4+4+2. This is due to...

[is this just a stylistic choice? or are there substantive implications?]

[3] It is possible that C1 is initially less tractable, then becomes more tractable than C2, shown in Fig 6 (C2 has stronger diminishing returns). In this case, C1 has a lower MU/$ at low values of $, but a higher MU/$ at high values of $. But this is not an example of low tractability being outweighed by low crowdedness, since tractability is changing with crowdedness.