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, (or, marginal cost-effectiveness). The Importance-Tractability-Neglectedness (ITN) framework has been used as a way of calculating 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:

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 depends on the context (in particular, resources spent). For example, AI risk might have had the highest in 2013, but the funding boost from OpenAI pushed it to a lower value of . 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, .

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.

I like this post, but calling the second concept in ITC tractability is confusing when everyone already knows ITN! Maybe it would have been better to call it something else, like "absolute tractability" or "attackability" or "doability" or something.

You think defining tractability as "% of problem solved / extra $" is confusing because the original 80k article defined it as "% of problem solved / % increase in resources"?

It adds confusion in that the term means two different things now and the original definition is more common. It subtracts confusion in that "% of problem solved / extra $" is more intuitive.

I think in everyday usage, people don't use "tractability" in such a precise way, so the slight change in definition doesn't add confusion.

I think some images don't display for me. This is what it looks like for me:

Okay, photos uploaded to Dropbox instead of Google Photos.

For future reference, this is what worked for me, using Dropbox:

I still can't see them. This is what it looks like now.

As mentioned here, copying images from Google Doc and pasting them seems to work reliably.

It would be good if there were more visible guides on how to post, as discussed in that thread.

Now they load.

The google docs method worked, but you can't control image size.

I'm now using imgur, which should be recommended somewhere here for authors.

Pictures still don't seem to be loading

Clicking on 'Open Image in New Tab' indicates that the image is hosted by Google Photos, so I suspect the privacy settings are preventing us from seeing them. Maybe Google read Rob's angry post and have now taken things to the other extreme. :P

None of the images display for me either. This is what it looks like for me:

Let's see how this works graphically. First, we start with tractability as a function of dollars (crowdedness), as in Figure 1. With diminishing marginal returns, "% solved/$" is decreasing in resources.

Next, we multiply tractability by importance to obtain MU/$ as a function of resources, in Figure 2. Assuming that Importance = "utility gained/% solved" is a constant[2], all this does is change the units on the y-axis, since we're multiplying a function by a constant.

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 to the highest MU/$ causes, ultimately equalizing MU/$ across all causes as diminishing returns take effect. (Note the similarity to the utility maximization problem from intermediate microeconomics, where you choose consumption of goods to maximize utility, given their prices and subject to a budget constraint.)

Update: The pictures load for me now

Nice article Michael. Improvements to EA cause prioritization frameworks can be quite beneficial and I'd like to see more articles like this.

One thing I focus on when trying to make ITC more practical is ways to reduce its complexity even further. I do this by looking for which factors intuitively seem to have wider ranges in practice. Impact can vary by factors of millions or trillions, from harmful to helpful, from negative billions to positive billions. Tractability can vary by factors of millions, from negative millionths to positive digits. The Crowdedness component generally implies diminishing or increasing marginal returns only vary by factors of thousands, from negative tens to positive thousands.

In summary the ranges are intuitively roughly:

Let's assume interventions have randomly associated with them samples from probability distributions over these ranges. Roughly speaking then we should care about these factors based on the degree to which they help us clearly see which intervention is better than another.

The extent to which these let us distinguish between the value interventions is based on our uncertainty per factor for each intervention and how the value depends on each factor. Because the value is equal to Importance*Tractability*CrowdednessAdjustmentFactor each factor is treated the same (there is abstract symmetry). Thus we only need to consider how big each factor range is in terms of our typical intervention factor uncertainty. This then tells us how useful each factor is at distinguishing interventions based on importance.

Pulling numbers out the the intuitive hat for the typical intervention uncertainty I get:

Dividing the ranges into these units lets us measure the distinguishing power of each factor:

As a rule of thumb then it looks like focusing on Importance is better than Tractability is better than Crowdedness. This lends itself to a sequence of improving heuristics for comparing the value of interventions then:

(The above analysis is only approximately correct and will depend on details like the precise probability distribution over interventions you're comparing and your uncertainty distributions over interventions for each factor.

The ITC framework can be further extended in several ways like: making precise curves interventions on the factors of ITC, extending the detail of the analysis of resources to other possible bottlenecks like time and people, incorporating the ideas of comparative advantage and market places, .... I hope someone does this!)

(PS I'm thinking of making this into a short post and enjoy writing collaborations so if someone is interested send me an EA forum message.)

Hi Justin, thanks for the comment.

I'm in favor of reducing the complexity of the framework, but I'm not sure if this is the right way to do it. In particular, estimating "importance only" or "importance and tractability only" isn't helpful, because all three factors are necessary for calculating MU/$. A cause that scores high on I and T could be low MU/$ overall, due to being highly crowded. Or is your argument that the variance (across causes) in crowdedness is negligible, and therefore we don't need to account for diminishing returns in practice?

My argument is about the later; the variances decrease in size from I to T to C. The unit analysis still works because the other parts are still implicitly there but treated as constants when dropped from the framework.

I guess I'm expecting diminishing returns to be an important factor in practice, so I wouldn't place much weight on an analysis that excludes crowdedness.

Michael, thanks for this post. I have been following the discussion about INT and prioritisation frameworks with interest.

Exactly how should I apply the revised framework you suggest? There are a number of equations, discussions of definitions and circularities in this post, but a (hypothetical?) worked example would be very useful.

Yes, the difficult part is applying the ITC framework in practice; I don't have any special insight there. But the goal is to estimate importance and the tractability function for different causes.

You can see how 80k tries to rank causes here.

One reason to keep Tractability separate from Neglectedness is to distinguish between "% of problem solved / extra dollars from anyone" and "% of problem solved / extra dollars from you".

In theory, anybody's marginal dollar is just as good as anyone else's. But by making the distinction explicit, it forces you to consider where on the marginal utility curve we actually are. If you don't track how many other dollars have already been poured into solving a problem, you might be overly optimistic about how far the next dollar will go.

I think this may be close to the reason Holden(?) originally had in mind when he included neglectedness in the framework.

I'm not sure I follow. In my framework, "how many other dollars have already been poured into solving a problem" is captured by crowdedness, ie., total resources allocated to the problem, ie., the position on the x-axis.

Fair point.