Progress and preservation in IDA

Iterated distillation and amplification (henceforth IDA) is a proposal for improving the capability of human-machine systems to suprahuman levels in complex domains where even evaluation of system outputs may be beyond unaugmented human capabilities. For a detailed explanation of the mechanics, I’ll refer you to the original paper just linked, section 0 of Machine Learning Projects for Iterated Distillation and Amplification, or one of the many other explanations floating around the Web.

We can view IDA as dynamic programming with function approximation¹ instead of a tabular cache. Just like the cache in dynamic programming, the machine learning component of IDA is a performance optimization. We can excise it and look at just the divide-and-conquer aspect of IDA in our analysis. Then this simplified IDA roughly consists of: (1) repeatedly decomposing tasks into simpler subtasks; (2) eventually completing sufficiently simple subtasks; and (3) aggregating outputs from subtasks into an output which completes the original, undecomposed task. We’ll examine this simplified model² in the rest of the post. (If you’d like a more concrete description of the divide-and-conquer component of IDA, there’s a runnable Haskell demo here.)

Safety is progress plus preservation

For type systems, the slogan is “safety is progress plus preservation”. Because we’re using this only as a cute analogy and organizing framework, we’ll not get into the details. But for type systems:

Progress

“A well-typed term is […] either […] a value or it can take a step according to the evaluation rules.”

Preservation

“If a well-typed term takes a step of evaluation, then the resulting term is also well typed.”

(Both from (Pierce and Benjamin 2002).)

We also need progress and preservation in IDA. Roughly:

Progress

A question is easy enough to be answered directly or can be decomposed into easier subquestions.

Preservation

The answer from aggregating subquestion answers is just as good as answering the original question.

Let’s try to make this more precise.

A corrected model suggests climate change interventions may be within a factor of two of direct cash transfers

In an earlier EA forum post, data from a new paper on country-level social cost of carbon is used to estimate the comparative cost-effectiveness of climate change interventions and global development interventions (cost-effectiveness of the latter as determined by GiveWell’s models). A central component of the earlier post (henceforth GDvCC¹) is supposed to be income²-weighting—$10 dollars of lost income means a great deal more in terms of utility for someone that makes $200 per year than for someone that makes $20,000 per year. More granular, country-level data on the social cost of carbon gets us closer to accounting for this distributional consideration³ and allows us to express the social cost of carbon in a way that’s directly comparable with the outputs of GiveWell’s models. GDvCC’s model finds that, in its “realistic” scenario, climate change interventions are 3% as cost-effective as GiveDirectly and 0.4% as cost-effective as GiveWell’s median top charity. However, I think there’s an error in the way the country-level social cost of carbon (CSCC) is interpreted in GDvCC which leads to incorrect income-weighting. Correcting for this error suggests that climate change interventions (again, under “realistic” assumptions) are 57% as cost-effective as GiveDirectly.

The Economic Lives of the Poor

The Economic Lives of the Poor is a 2007 paper by 2019 Nobel Laureates¹ Abhijit Banerjee and Esther Duflo. It describes results from household surveys of the poor (less than $2.16 a day in 1993 PPP dollars) and extremely poor (less than $1.08 a day in 1993 PPP dollars) conducted in Cote d’Ivoire, Guatemala, India, Indonesia, Mexico, Nicaragua, Pakistan, Panama, Papua New Guinea, Peru, South Africa, Tanzania, and Timor Leste (East Timor). What follows is a condensation of that paper highlighting the most important and striking claims. I focus on the descriptive part of the paper and omit the second part of the paper investigating some concomitant economic puzzles.

Living arrangements

Extended families are common among the extremely poor with the median household containing between seven and eight members. The population tends to be young with only about one quarter as many over 51s as 21–50s (In the U.S., the ratio is 0.6 rather than ~0.25.).

Spending

Food and other consumption purchases

Food expenditures typically represent between one half and three quarters of the budget.² Expenditure on alcohol and tobacco ranges from about 1 percent to about 8 percent. The median extremely poor household in Udaipur spent 10 percent of its budget on festivals, but expenditure on movies, theater and shows is less than 1 percent.

Ownership of assets

Land ownership among the extremely poor ranges from 4 percent in Mexico to 99 percent in Udaipur. However, the owned plots are often small—less than three hectares—and of poor quality.

“In Udaipur, where we have detailed asset data, most extremely poor households have a bed or a cot, but only about 10 percent have a chair or a stool and 5 percent have a table. […] No one has a phone.”

Health and well-being

The bottom decile of income in an Indian survey sample averages 1400 calories a day. Sixty-five percent of poor adults in Udaipur have a BMI that classifies them as underweight and 55 percent are anemic.

Between 11 and 46 percent (depending on the country) of the extremely poor report having been bedridden for at least one day in the the last month.

“While the poor certainly feel poor, their levels of self-reported happiness or self-reported health levels are not particularly low (Banerjee, Duflo, and Deaton, 2004). On the other hand, the poor do report being under a great deal of stress, both financial and psychological.”

Assorted links XV

1. Tacit Knowledge, Trust and the Q of Sapphire

Much more interesting IMO than these short excerpts will suggest:

For about 20 years, the team led by Vladimir Braginsky at Moscow State University, as part of a larger programmeon low dissipation systems, has been claiming to have measured quality factors (Qs) in sapphire up to 4x10^8 at room temperature. The ‘quality factor’ of a material indicates the rate of decay of its resonances — how long it will ‘ring’ if struck. […] But until the summerof 1999, no one outside Moscow State had succeeded in measuring a Q in sapphire higher than about 5x10’.

In the summer of 1998, after a series of failed efforts to measure Qs comparable to the Russian claims, members of a Glasgow University group visited Moscow State University for a week to learn the Russian technique. […] In neither case was a high-Q measurement achieved. Nevertheless, after only a few days in Russia, the Glasgow team had become convinced that the Russian results were correct.

2. First, do harm

Studies that deliberately infect people with diseases are on the rise. They promise speedier vaccine development, but there’s a need to shore up informed consent.

3. Moral Bias and Corrective Practices: A Pragmatist Perspective

Thus, the moral biases of slavery advocates proved largely immune to correction by the dominant methods of moral philosophy, which were deployed by white abolitionists. Ascent to the a priori led to abstract moral principles—the Golden Rule, the equality of humans before God—that settled nothing because their application to this world was contested. Table-turning exercises were ineffective for similar reasons. Reflective equilibrium did not clearly favor the abolitionists, given authoritarian, Biblical, and racist premises shared by white abolitionists and slavery advocates. No wonder only a handful of Southern whites turned against slavery on the basis of pure moral argument.

4. A Panel Data Analysis of the Fungibility of Foreign Aid

The donor community has been increasingly concerned that development assistance intended for crucial social and economic sectors might be used directly or indirectly to fund unproductive military and other expenditures. The link between foreign aid and public spending is not straightforward because some aid may be “fungible.” This article empirically examines the impact of foreign aid on the recipient’s public expenditures, using cross-country samples of annual observations for 1971-90

5. In Soviet Union, Optimization Problem Solves You

The most plausible candidate [to making linear programming solutions feasible for economic planning problems] is to look for problems which are “separable”, where the constraints create very few connections among the variables. If we could divide the variables into two sets which had nothing at all to do with each other, then we could solve each sub-problem separately, at tremendous savings in time. The supra-linear, \(n^{3.5}\) scaling would apply only within each sub-problem. We could get the optimal prices (or optimal plans) just by concatenating the solutions to sub-problems, with no extra work on our part.

Unfortunately, as Lenin is supposed to have said, “everything is connected to everything else”. […] A national economy simply does not break up into so many separate, non-communicating spheres which could be optimized independently.

So long as we are thinking like computer programmers, however, we might try a desperately crude hack, and just ignore all kinds of interdependencies between variables. If we did that, if we pretended that the over-all high-dimensional economic planning problem could be split into many separate low-dimensional problems, then we could speed things up immensely, by exploiting parallelism or distributed processing. […]

At this point, each processor is something very much like a firm, with a scope dictated by information-processing power, and the mis-matches introduced by their ignoring each other in their own optimization is something very much like “the anarchy of the market”.

The reliability of moral judgments: A survey and systematic(ish) review

(This post is painfully long. Coping advice: Each subsection within Direct (empirical) evidence, within Indirect evidence, and within Responses is pretty independent—feel free to dip in and out as desired. I’ve also put a list-formatted summary at the end of each these sections boiling down each subsection to one or two sentences.)

Intro

Dan is a student council representative at his school. This semester he is in charge of scheduling discussions about academic issues. He often picks topics that appeal to both professors and students in order to stimulate discussion.

Is Dan’s behavior morally acceptable? On first glance, you’d be inclined to say yes. And even on the second and third glance, obviously, yes. Dan is a stand-up guy. But what if you’d been experimentally manipulated to feel disgust while reading the vignette? If we’re to believe (Wheatley and Haidt 2005), there’s a one-third chance you’d judge Dan as morally suspect. ‘One subject justified his condemnation of Dan by writing “it just seems like he’s up to something.” Another wrote that Dan seemed like a “popularity seeking snob.”’

The possibility that moral judgments track irrelevant factors like incidental disgust at the moment of evaluation is (to me, at least) alarming. But now that you’ve been baited, we can move on the boring, obligatory formalities.

Uncertainty and sensitivity analysis of GiveWell's top charity rankings

In the last two posts, we performed uncertainty and sensitivity analyses on GiveWell’s charity cost-effectiveness estimates. Our outputs were, respectively:

• probability distributions describing our uncertainty about the value per dollar obtained for each charity and
• estimates of how sensitive each charity’s cost-effectiveness is to each of its input parameters

One problem with this is that we are not supposed to take the cost-effectiveness estimates literally. Arguably, the real purpose of GiveWell’s analysis is not to produce exact numbers but to assess the relative quality of each charity evaluated.

Another issue is that by treating each cost-effectiveness estimate as independent we underweight parameters which are shared across many models. For example, the moral weight that ought to be assigned to increasing consumption shows up in many models. If we consider all the charity-specific models together, this input seems to become more important.

Metrics on rankings

We can solve both of these problems by abstracting away from particular values in the cost-effectiveness analysis and looking at the overall rankings returned. That is we want to transform:

into:

But how do we usefully express probabilities over rankings¹ (rather than probabilities over simple cost-effectivness numbers)? The approach we’ll follow below is to characterize a ranking produced by a run of the model by computing its distance from the reference ranking listed above (i.e. GiveWell’s current best estimate). Our output probability distribution will then express how far we expect to be from the reference ranking—how much we might learn about the ranking with more information on the inputs. For example, if the distribution is narrow and near 0, that means our uncertain input parameters mostly produce results similar to the reference ranking. If the distribution is wide and far from 0, that means our uncertain input parameters produce results that are highly uncertain and not necessarily similar to the reference ranking.

Spearman’s footrule

What is this mysterious distance metric between rankings that enables the above approach? One such metric is called Spearman’s footrule distance. It’s defined as:

In other words, the footrule distance between two rankings is the sum over all items of the (absolute) difference in positions for each item. (We also add a normalization factor so that the distance varies ranges from 0 to 1 but omit that trivia here.)

So the distance between A, B, C and A, B, C is 0; the (unnormalized) distance between A, B, C and C, B, A is 4; and the (unnormalized) distance between A, B, C and B, A, C is 2.

Kendall’s tau

Another common distance metric between rankings is Kendall’s tau. It’s defined as:

In other words, the Kendall tau distance looks at all possible pairs across items in the rankings and counts up the ones where the two rankings disagree on the ordering of these items. (There’s also a normalization factor that we’ve again omitted so that the distance ranges from 0 to 1.)

So the distance between A, B, C and A, B, C is 0; the (unnormalized) distance between A, B, C and C, B, A is 3; and the (unnormalized) distance between A, B, C and B, A, C is 1.

Angular distance

One drawback of the above metrics is that they throw away information in going from the table with cost-effectiveness estimates to a simple ranking. What would be ideal is to keep that information and find some other distance metric that still emphasizes the relationship between the various numbers rather than their precise values.

Angular distance is a metric which satisfies these criteria. We can regard the table of charities and cost-effectiveness values as an 8-dimensional vector. When our output produces another vector of cost-effectiveness estimates (one for each charity), we can compare this to our reference vector by finding the angle between the two².

Sensitivity analysis of GiveWell's cost-effectiveness analysis

Last time we introduced GiveWell’s cost-effectiveness analysis which uses a spreadsheet model to take point estimates of uncertain input parameters to point estimates of uncertain results. We adjusted this approach to take probability distributions on the input parameters and in exchange got probability distributions on the resulting cost-effectiveness estimates. But this machinery lets us do more. Now that we’ve completed an uncertainty analysis, we can move on to sensitivity analysis.

Sensitivity analysis

The basic idea of sensitivity analysis is, when working with uncertain values, to see which input values most affect the output when they vary. For example, if you have the equation \(f(a, b) = 2^a + b\) and each of \(a\) and \(b\) varies uniformly over the range from 5 to 10, \(f(a, b)\) is much more sensitive to \(a\) then \(b\). A sensitivity analysis is practically useful in that it can offer you guidance as to which parameters in your model it would be most useful to investigate further (i.e. to narrow their uncertainty).

Visual sensitivity analysis

The first kind of sensitivity analysis we’ll run is just to look at scatter plots comparing each input parameter to the final cost-effectiveness estimates. We can imagine these scatter plots as the result of running the following procedure many times¹: sample a single value from the probability distribution for each input parameter and run the calculation on these values to determine a result value. If we repeat this procedure enough times, it starts to approximate the true values of the probability distributions.

(One nice feature of this sort of analysis is that we see how the output depends on a particular input even in the face of variations in all the other inputs—we don’t hold everything else constant. In other words, this is a global sensitivity analysis.)

(Caveat: We are again pretending that we are equally uncertain about each input parameter and the results reflect this limitation. To see the analysis result for different input uncertainties, edit and run the Jupyter notebook.)

Direct cash transfers

GiveDirectly

The scatter plots show that, given our choice of input uncertainty, the output is most sensitive (i.e. the scatter plot for these parameters shows the greatest directionality) to the input parameters: