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 dis­cuss some is­sues with the cur­rent frame­work, pro­pose a mod­ified ver­sion, and con­sider a few im­pli­ca­tions.

80,000 Hours 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.[1] 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? This should go with­out say­ing.

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), uses an ab­solute rather than a rel­a­tive stan­dard, and avoids the prob­lem of hav­ing the tech­ni­cal defi­ni­tion con­flict with the ev­ery­day mean­ing.

Thus, our re­vised frame­work is now ITC:

  • Im­por­tance = util­ity gained /​ % of prob­lem solved

  • Tractabil­ity = % of prob­lem solved /​ ex­tra $

  • Crowd­ed­ness = $ al­lo­cated to the problem

So how does crowd­ed­ness fit into this setup, if it’s not part of the main defi­ni­tion? 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.

A graph­i­cal approach

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.)

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 $.

Implications

(1) All three fac­tors in the ITC frame­work are nec­es­sary to draw a con­clu­sion about which cause is best. Con­sider this pas­sage from the 80k ar­ti­cle:

[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/​$. If other things are not equal, the cause with more re­sources may have a higher or lower MU/​$. (And gen­er­ally, if a cause scores low on one of the three fac­tors, it can still have the high­est MU/​$, through high scores on one or both of the other two fac­tors.)

(2) With this setup, we can clearly see how MU/​$ de­pends on con­text (in par­tic­u­lar, re­sources spent). To make up a hy­po­thet­i­cal ex­am­ple, AI risk might have had the high­est MU/​$ in 2013, but the fund­ing boost from OpenAI pushed it down the tractabil­ity curve 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, .

(3) 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.

(4) The sys­temic change cri­tique ar­gues that the stan­dard cause pri­ori­ti­za­tion frame­work can­not han­dle in­creas­ing marginal re­turns. For ex­am­ple, large-scale poli­ti­cal re­form yields no re­sults un­til a crit­i­cal mass is reached and mas­sive change oc­curs. But in fact this is eas­ily mod­eled as a tractabil­ity func­tion (Fig. 1) that is in­creas­ing for some part of its do­main. That is, when near­ing the crit­i­cal mass, each ad­di­tional dol­lar solves a larger per­cent of the prob­lem than the pre­vi­ous dol­lar. While this case re­quires a differ­ent de­ci­sion rule than “al­lo­cate re­sources to the cause with the high­est MU/​$”, it is a straight­for­ward ex­ten­sion of the stan­dard model.

Conclusion

I pro­pose a model of cost-effec­tive­ness us­ing Im­por­tance, Tractabil­ity, and Crowd­ed­ness. Tractabil­ity is a func­tion of crowd­ed­ness, and mul­ti­ply­ing im­por­tance and tractabil­ity gives us marginal util­ity per dol­lar. So is the 80k model wrong? No. I sim­ply find it more in­tu­itive to think about tractabil­ity as “% of prob­lem solved /​ ex­tra $” in­stead of “% of prob­lem solved /​ % in­crease in re­sources”, and this is the re­sult­ing model.


Notes

[1] Also, the Ne­glect­ed­ness term “% in­crease in re­sources /​ ex­tra $” is always equal to (1/​re­sources)%, which seems a bit re­dun­dant. That is, given re­sources, an ex­tra dol­lar always in­creases your re­sources by . Eg, given $100, an ex­tra dol­lar in­creases your re­sources by 1%.

[2] This seems to be a defi­ni­tional is­sue: we can define im­por­tance as a con­stant, 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 en­tire prob­lem.