It is of course important to look at whether or not what you are measuring validly predicts what you are trying to predict. Despite much worry about SAT coaching courses, I get the very strong impression that the young people who score highest on the SAT are still, after all these decades, the young people who read widely for fun and who think about math problems for fun, just as they were in the 1970s when young people in my region of the United States were not coached for the SAT at all. The standardized conditions for administering the SAT have always included (in my lifetime) giving students registered for the test access to a complete previously administered test to serve as practice material. According to a psychometrician I know, precisely because the SAT allows everyone to practice in advance, it is an especially valid estimate of the test-taker's general ability to learn and to reason.

You can look up research about SAT correlations with general intelligence[1] and IQ test scores[2] and college grades[3] (what SAT scores are intended to predict) on Google Scholar and see for yourself what the empirical research says. No one-factor means of predicting college success is perfect (and if college admission officers were forced to use ONE factor to admit applicants to college, the factor they would be wise to choose to predict college grades is UNWEIGHTED high school grade average), but SAT scores (or ACT scores) are still used in the admission process of most colleges that are at all selective because they provide helpful information for comparing applicants who attended different high schools.

If you would like to put names of particular researchers into a Google Scholar search to find out what they have discovered about current use of SAT tests, I would suggest Nathan Kuncel or Paul Sackett, both of whom have studied quite a few detailed data sets about SAT-takers and what their scores predict.

AFTER EDIT: Terence Tao, in the interview kindly posted to open this thread, makes the important point that sometimes teachers entertain more than they actually teach. (I think a lot of commercial test-prep courses have this defect.) He said, "Sometimes making a class more enjoyable or entertaining is not the same as making it more educational. I remember once when I taught calculus, one of the sections was quadric surfaces, like ellipsoids, paraboloids and so forth. So there’s this thing called a hyperbolic paraboloid, and I wanted to demonstrate this. It turns out that a Pringle has the shape of a hyperbolic paraboloid. So I brought in a pack of Pringles to class and said, 'this is a hyperbolic paraboloid, this is what it looks like.' I ate the Pringle as I was writing equations on the board. Well many years later, I ran into someone on the street who said, 'Oh, I know you. I took one of your classes. I forget what it was, but there was a Pringle.' So I thought, 'you didn’t remember any of the math, but you remember the Pringle.' So it didn’t really work." Following up on that in the context of this subthread, I think a lot of students know who Joe Bloggs[4] is without being able to reason successfully to find the right answer choice on the harder SAT questions.

[1] http://scholar.google.com/scholar?hl=en&q=SAT+general+intell...

[2] http://scholar.google.com/scholar?q=SAT+IQ+test

[3] http://scholar.google.com/scholar?q=SAT+college+grades

[4] http://books.google.com/books?id=K4SteOicBAQC&pg=PA23&lpg=PA...

This is true in most of social science. Metrics work when people don't know they're being measured. Once people learn they're being measured on something, they optimize to it.

On another note... If a metric is being used properly, it might not seem like it's working. For example... Harvard saw that GMATs didn't correlate with their MBA's success, so they dropped it as admission criteria. Years later they checked the GMAT scores for the classes where they weren't required. What happened? GMATs correlated to performance. What's the cause? Earlier on they were properly weighting in. (Higher GPA? GMAT doesn't matter much. Lower GPA? It matter mores. Grad degree in stats? Lower undergrad GPA and GMAT don't matter as much, etc.) If you're weighting it properly, the importance won't show. (In essence, a 780 is the right marginal score to let one person in, a 680 on another)

All that said, in a way, the perfect measure is an unfair one, because you don't know what you're being measured on so you can't change it.

That is partially true. A metric should continue to "work" when people know they are being measured on it. A good metric is one which makes the measured person more effective when they explicitly try to optimize it.

So for example, pro basketball player knows they are measured by their accuracy. However, when a player optimizes his accuracy, that does not compromise the effectiveness of that metric.

The important thing here is that a metric that is a _correlate_ of the thing you care about but can't measure directly might start to work less well once people know you're measuring it. And the reason is that the correlation with the thing you really care about might decrease.

To use your basketball example, say you have a player that takes a shot every time they get close enough to the basket, scoring 60% of them. You decide to measure accuracy. They get more conservative with when they take shots, so now half the time they run out of shot clock (resulting in a turnover) and the other half of the time they take a shot and score with 100% accuracy.

Their accuracy went from 60% to 100%, but the fraction of time possession results in scoring went from 60% to 50%.

The issue there is that you don't _really_ care about accuracy per se. What you care about is contribution to the score differential vs the opposing team. But that's hard to quantify, so people come up with various metrics that correlate to such contribution (shooting accuracy, rebound percentage, etc, etc), along with relative weights for these metrics. In fact, the weights depend on the exact team you're playing, who your current teammates are, etc.

In any case, it's actually fairly rare to be able to directly measure the thing you care about, especially in the social sciences, not least because a lot of the things we care about ("success in life", "college preparedness", "job satisfaction", "knowledge and understanding of the material covered by this class") are fairly difficult to quantify. So instead one ends up measuring various correlates and hoping that either people don't adjust their behavior too much to degrade the correlation before you're done measuring or that your measurement process attempts to account for such adjustments.

I was thinking similarly. If you pay salespeople only on Sales $, it sounds like incentives are aligned, but you have to watch yourselves.

Indeed. Just yesterday a buddy told me of how he knew someone a few years ago (great story I know) who was gaming telephone subscriptions. He'd go into the system and check a box, say 'extra 500 minutes' with a deal that gave the first 3 months for free. This is normally what you do after you close such a sale when a customer buys the extra deal, you go into the system and register it. Only now he'd just do it without the customer knowing. 3 months later he'd cancel it. His sale was still registered and his customer never knew or ever paid, and he got his sales bump.

And another friend of mine works at a big software company (SAP, Oracle, those sorts of companies) in sales. Basically he has to generate leads, pass them on, and if they're closed he hits his target. So what most people do is they call the manager and suck up to him, and ask him to register a closed sale's lead as one of his. A lot of these sales are simply recurring sales, or sales closed when a customer called the company, as opposed to closed after a cold-call led to a lead. Long story short, you've got people hitting their targets without generating any leads or sales, making $40k a year and moving into the same closing function two years later without ever having done anything.

The idea seems pretty straightforward, once you create a metric, people will game it. And it seems a single person designing the system (the metrics, the governance of the metrics) over time continuously gets outsmarted by the hundreds or even thousands of people that are incentivized to find the loophole in the design of that individual.

Test preparation does not do much to increase SAT scores:

"For students that have taken the test before and would like to boost their scores, coaching seems to help, but by a rather small amount. After controlling for group differences, the average coaching boost on the math section of the SAT is 14 to 15 points. The boost is smaller on the verbal section of the test, just 6 to 8 points. The combined effect of coaching on the SAT for the NELS sample is about 20 points."

http://nepc.colorado.edu/files/Briggs_Theeffectofadmissionst...

I went through the Princeton Review many years ago and it improved my score by about 200 points.

Maybe I'm an outlier, but I can tell you this: nobody would pay for or go through the course if the expected boost was 20 points.

On the other hand, if I hadn't taken the Princeton Review, I'd have done something else to prep. And who knows how much I'd have been able to improve on my own.

They did not measured whether it is possible to prepare for SAT. They measured whether commercial courses boost your score. The comparison is not between student who does no additional work for SAT and the one who study a lot. The comparison is between student enrolled paying coach and the one who is not paying special SAT coach. The latter one can still work a lot with help of books and websites.

It does not mean you can not prepare for SAT, it just means that money spent on commercial coach are probably wasted. It says nowhere that if you skip all preparation altogether, you will get good result.

Quote: "Most studies have focused on estimating the effect of one specific type of test preparation, known as “coaching.” In this analysis, students Students have been coached if they have enrolled in a commercial preparation course not offered by their school but designed specifically for the SAT or ACT. The distinction made here is whether a test-taker has received systematic instruction over a short period of time. Preparation with books, videos and computers is excluded from the coaching definition because while the instruction may be systematic, it has no time constraint. Preparation with a tutor is excluded because while it may have a time constraint, it is difficult to tell if the instruction has been systematic."

Article conclusion focus on coached students only.

Note the time constraint in the above quote. People who take those tests seriously not only take the short course, but probably focused on the test long before the course started. At least, that is how well performing students I knew years ago behaved. The course itself might have boost their score only a little, but their preparation consisted of much more then just one course. After all, they are adults about to enter college - they are expected to be able to learn alone.

Most coaching is really poor. I used to do math prep for the SAT and I consistently improved scores more than the data would predict. After sitting through Princeton Review, it was easy to see why.

I suspect those that benefit the most from prep aren't telling.

Sounds like Google's toolbar pagerank, which was a neat way of seeing the very generic "relevance" score Google assigned to a page.

Then Search Engine Optimization really started catching ground, and some SEO's would obsess about that number, going through all kinds of work to manage that number, and basing business decisions (such as: should we link to this site? should we request a link from that site?) far too heavily on that number, as opposed to the actual business relevance of what they were doing, and as opposed to whether it would be a useful result for their own visitors (or those of the other site).

> control purposes

Here you have an implicit assumption that the system being controlled can react, that is, in the sense of control theory, change its plant dynamics, due to the effort of the control. Well, for a lot of work in control, say, in most aerospace applications, that assumption is false or essentially so. Then getting a good metric and using it is fine.

E.g., get the power spectrum of ocean wave noise and use that in a control system to keep a submarine at essentially a constant depth. We don't expect that the metric of the ocean wave power spectrum and the control system in the submarine will change the ocean very much!

E.g., GPS is a terrific metric, but we don't expect that using it will change the shape of the earth.

Etc.

Certain things cannot be gamed, or even if they're gamed, they're still good, like your IQ score.

You can improve your IQ score by taking lots of IQ tests (your "IQ" will slowly improve), and I don't consider IQ to be a good thing by itself.

Not really -- the IQ tests used by MENSA for example are quite reliable/stable. You can improve your result by 6-10 points with a lot of training, but that's usually the most that people can achieve.

A standard deviation on IQ tests is 15 points. A 6-10 point improvement from the median represents a jump of 15.5 - 24.75 percentile rank. Even at the level MENSA is looking at, someone with a 10 point improvement could have a "true IQ" at just above the 95th percentile and qualify for their 98th percentile cutoff.

Maybe the reason MENSA's tests are reliable is that not many people are interested in joining MENSA - I am not denying that MENSA can be of interest, but its admittance would not be worth preparing IQ tests like crazy.

On the other hand, if IQ tests were used for admissions in prestigious universities, you can bet some students will train specifically for IQ tests.

Maybe they'd all get a bit smarter as a result?

I'm truly impressed by the cognitive dissonance here. On the one hand, this is a wildly popular platitude for intellectuals to endorse, and Terry Tao would certainly suffer some social penalties if he strongly opposed it. On the other hand, if this claim were actually true, it would invalidate basically the entire field of mathematical optimization and decision theory.

It's also strange that proponents of this view rarely apply it uniformly. There are many metrics that are quite popular among proponents of Goodhart's law - for instance, CO2 emissions, capital reserve requirements, etc.

(Also SAT prep barely works http://online.wsj.com/news/articles/SB124278685697537839?mg=... - it's the "well rounded" portion of college applications that people spend the most time gaming.)

"On the other hand, if this claim were actually true, it would invalidate basically the entire field of mathematical optimization and decision theory."

I might be able to help by pointing out that a technology that depends on random sampling of small components of "intelligence" or whatever is going to be totally screwed up if the sampling is no longer random and now the outcome of the test depends mostly on the amount of money spent on prep classes.

From manufacturing I can predict a lot about the quality of something in general off just one graph of the distribution of length of one part compared to other manufacturers graphs of the same single measurement on the same part, but if the mfgr "cooks the books" by optimizing one measurment of that part to perfection while taking away labor from other areas of part quality, then my comparisons will be useless, especially when comparing optimizers vs non-optimizers.

I'm not sure your strong criticism of Goodhart's Law is quite fair. It is stated so as to be pithy, but I think it is fairly obviously meant to be applied only to those situations where the thing being measured in some sense "judges itself" by that score, and adjusts its performance to try and improve that score.

This is quite likely the case with school children, but often not the case with, say, industrial processes. If, however, you make someone's job dependent on meeting some particular target for that process, then a feedback loop is created that can lead to the kinds of problems being discussed.

If the feedback loop isn't there, then the metric will remain as useful as it ever was. So the point is, be wary of unintentional feedbacks in your system, not some grandiose rejection of the possibility of optimisation.

Do you believe a company running an industrial process will not "judge itself" by it's CO2 emissions, or that a bank will not adjust to meet capital reserve requirements?

Yes, I do believe that they will, and those judgments can reduce the effectiveness of legislation as it is originally conceived. I only see that as speaking to the point, not against it.