Thanks, really like this point (which I've kind of applied many times but not had such a clean articulation of).

I think it's important to remember that the log returns model is essentially an ignorance prior^[1]. If you understand things about the structure of the problem at hand you can certainly depart from it. e.g. when COVID emerged, nobody had spent any time trying to find and distribute a COVID vaccine. But it will be obvious that going from $1 million to $2 million spent won't give you an appreciable chance of solving the problem (since there's no way that could cover distributing things to billions of people), whereas going from $100 billion to $200 billion spent would do. Often early work can be valuable because it can spur future spending (so you might recover something like log returns in expectation), but in this case it was obvious that there would be much more than $2 million future spending whatever the early work did.

1. ^{^}

   Well ... also some problems which are solved via lots of little contributions actually have ex post log returns, rather than log returns just being an ex ante thing. But that's a significantly smaller class of problems.

Thanks, this is a good post. A half-baked thought about a related but (I think) distinct reason for this phenomenon: I wonder if we tend to (re)define the scale of problems such that they are mostly unsolved at present (but also not so vast that we obviously couldn't make a dent). For instance, it's not natural to think that the problem of 'eradicating global undernourishment' is more than 90% solved, because fewer than 10% of people in the world are undernourished. As long as problems are (re)defined in this way to be smaller in absolute terms, then tractability is going to (appear to) proportionally increase, as a countervailing factor to diminishing returns from extra investment of resources. A nice feature of ITN is that (re)defining the scale of a problem such that it is always mostly unsolved at present doesn't affect the bottom line of utility per marginal dollar, because (utility / % of problem solved) increases as (% of problem solved / marginal dollar) decreases. To the extent this is a real phenomenon, it could emphasise the importance of not reading too much into direct comparisons between tractability across causes.

Cluelessness can be another reason something is intractable. For example, effects on wild animal are really complicated, especially when population sizes change, and we know little about animals' welfare and have considerable uncertainty about their moral weights. As such, it's hard to know whether a given intervention is net positive or net negative in expectation. However, little has been spent on understanding the welfare of wild animals or their moral weights, so maybe this deep uncertainty is not unresolvable.

Luke Muehlhauser also said that almost all AI (governance) interventions he looks into are as likely to be net negative as they are to be net positive: https://forum.effectivealtruism.org/posts/pxALB46SEkwNbfiNS/the-motivated-reasoning-critique-of-effective-altruism?commentId=6yFEBSgDiAfGHHKTD

each additional doubling will solve a similar fraction of the problem, in expectation

Aren't you assuming the conclusion here?

I was in the process of writing a comment trying to debunk this. My counterexample didn't work so now I'm convinced this is a pretty good post. This is a nice way of thinking about ITN quantitatively. 

The counterexample I was trying to make might still be interesting for some people to read as an illustration of this phenomenon. Here it is:

Scale "all humans" trying to solve "all problems" down to "a single high school student" trying to solve "math problems". Then tractability (measured as % of problem solved / % increase in resources) for this person to solve different math problems is as follows:

• A very large arithmetic question like "find 123456789123456789^2 by hand" requires ~10 hours to solve
• A median international math olympiad question probably requires ~100 hours of studying to solve 
• A median research question requires an undergraduate degree (~2000 hours) and then specialized studying (~1000 hours)  to solve
• A really tough research question takes a decade of work (~20,000 hours) to solve
• A way ahead of its time research question (maybe, think developing ML theory results before there were even computers) I could see taking 100,000+ hours of work 

Here tractability varies by 4 orders of magnitude (10-100,000 hours) if you include all kinds of math problems. If you exclude very easy or very hard things (as Thomas was describing) you end up with 2 orders of magnitude (~1000-100,000 hours). 

I think this argument makes a lot of sense when applied to domains with a certain level of existing resources, but not for fields which are so neglected that there are virtually no resources spent there right now. In other words, I think the logarithmic returns framework breaks down for really high neglectedness, for two reasons:

1. High neglectedness is a signal of unusually high intractability - e.g. the "no plan of attack" case you describe, but also more subtle barriers. For example, we might have a brilliant intervention to reduce air pollution in China, but foreign funding regulations might be such a bottleneck that we couldn't actually spend any of that.

2. High neglectedness means there is not a lot of infrastructure to absorb the money needed to solve the problem. For example, I wrote about extreme heat adaptation for the Cause Exploration Prizes, and ultimately assessed that it could not be an area for giving simply because I could not find any organizations that work on extreme heat adaptation, so there was simply nowhere to spend money. You could argue that over a sufficiently long period, money could be used to create that infrastructure e.g. incubate organizations, but it's an open question to me resource-elastic that is and intuitively it doesn't feel logarithmic.

So in a perverse way, high neglectedness (which is generally desirable) is usually correlated with low tractability, and possibly tractability outside the logarithmic framework.

I'm curious whether people have thoughts on whether this analysis of problem-level tractability also applies to personal fit. I think many of the arguments here naively seems like it should apply to personal fit as well. Yet many people (myself included) make consequential career- and project- selection decisions based on strong intuitions of personal fit. 

This article makes a strong argument that it'd be surprising if tractability (but not importance, or to a lesser degree neglectedness) can differ by >2 OOMS. In a similar vein, I think it'd also be surprising if personal fit can differ by 2 OOMs. 

I'd be interested in theoretical arguments or empirical evidence here, in either direction (Note that showing someone has an absolute advantage of >100X over someone else in the same field is relatively little evidence to me, as the important question here is comparative advantage as conferred by personal fit).

I don't know if I understand why tractability doesn't vary much. It seems like it should be able to vary just as much as cost-effectiveness can vary. 

For example, imagine two problems with the same cost-effectiveness, the same importance, but one problem has 1000x fewer resources invested in it. Then the tractability of that problem should be 1000x higher [ETA: so that the cost-effectiveness can still be the same, even given the difference in neglectedness.]

Another example:  suppose an AI safety researcher solved AI alignment after 20 years of research. Then the two problems "solve the sub-problem which will have been solved by tomorrow" and "solve AI alignment" have the same local cost-effectiveness (since they are locally the same actions), the same amount of resources invested into each, but potentially massively different importances. This means the tractabilities must also be massively different.

These two examples lead me to believe that in as much as tractability doesn't vary much, it's because of a combination of two things:

1. The world isn't dumb enough to massively underinvest in a really cost-effective and important problems
2. The things we tend to think of as problems are "similarly sized" or something like that

I'm still not fully convinced, though, and am confused for instance about what "similarly sized" might actually mean.

 

Let the "baseline" level of tractability be a 10% chance to be solved with one doubling of resources.

Do you interpret this as "one doubling of resources increases the probability of solving the problem by 10 percentage points"? (Or, solves an additional 10% of the problem, for a problem that is continuous instead of binary.)

I argue that Bernard must be implicitly claiming that cause B is unusually tractable, that there is a strong departure from logarithmic returns, or that there is no feasible plan of attack for cause A.

Related: Rob Bensinger says MIRI's current take on AI risk is "we don't see a promising angle of attack on the core problem".

Suppose your problem is a huge pile of trash in your backyard; the best way to solve it is to pay people to haul away the trash, and the cost of this is roughly linear in the amount of trash removed.

Isn't this an example with diminishing returns? You can only fit so many trucks/people in your backyard, so you run into a bottleneck.

If problems don't differ dramatically in tractability, does that imply that we should be able to completely solve problems pretty easily?