Negative and Positive Selection

(Originally posted to my blog, The Rationalist Conspiracy; cross-posted here on request of Lukeprog.)

You’re the captain of a team, and you want to select really good players. How do you do it?

One way is through what I call positive selection. You devise a test – say, who can run the fastest – and pick the people who do best. If you want to be really strict, like if you’re selecting for the Olympics, you only pick the top fraction of a percent. If you’re a player, and you want to get selected, you have to train to do better on the test.

The opposite method is negative selection. Instead of one test to pick out winners, you design many tests to pick out losers. You test, say, who can’t run very well when it’s hot out, and get rid of them. Then you test who can’t run very well when it’s cold out, and get rid of them. Then you test running in the rain, and get rid of the losers there. And so on and so forth. When you’re strict with negative selection, you have lots and lots of tests, so that it’s very hard for any one person to pass through all the filters.

I think a big part of where American society’s gone wrong over the last hundred years is the ubiquitous use of negative selection over positive selection. (Athletics is one of the only exceptions. It’s apparently so important that people really care about performance – as opposed to, say, in medicine, where we exclude brilliant doctors if they don’t have the stamina to work ninety hours a week.) A single test can always be flawed; for example, IQ tests and SATs have many flaws. However, with negative selection, how badly you do is determined by the failure rate of every test combined. If you have twenty tests, and even one of them is so flawed it excludes good players, then your team will suck.

Elite college admissions is an example of a negative selection test. There’s no one way you can do really, really well, and thereby be admitted to Harvard. Instead, you have to pass a bunch of different selection filters: Are your SATs good enough? Are your grades good enough? Is your essay good enough? Are your extracurriculars good enough? Are your recommendations good enough? Failure on any one step usually means not getting admitted. And as competition has intensified, colleges have added more and more filters, like the supplemental applications top schools now require (in addition to the Common Application). It wasn’t always this way – Harvard used to admit primarily based on an entrance exam – until they discovered this let too many Jews in (no, seriously). More recently, the negative selection has been intensified by eliminating the SAT’s high ceiling.

Academia is another example of negative selection. To get tenure, first you have to get into a top PhD program. Then you have to graduate. Then you have to get a good recommendation from your advisor. Then you have to get a good postdoc. Then you have to get another good postdoc. Then you have to get a good assistant professorship. Then you have to get approved by the tenure committee. For the most part, if even one of those steps goes wrong – if you went to a second-tier PhD program, say – there’s no way to recover. Once you’re off the “track”, you’re off, and there’s no getting back on. It’s fail once, fail forever.

Grades are another example – A is a good grade, but there’s no excellent grade. There’s no grade that you only get if you’re in the top 0.1%. Hence, getting a really good GPA doesn’t mean excelling, so much as it means never failing. If you’re in high school and are taking six classes, if you fail one, your GPA is now 3.3 or less, regardless of how good you are otherwise.

In any field, at the top end, you tend to get a lot of variance. (Insert tales of the mad artist and mad mathematician.) Negative selection suppresses variance, by eliminating many of the dimensions on which people vary. Students at Yale are, for the most part, all strikingly similar – same socioeconomic class, same interests, same pursuits, same life goals, even the same style of dress. A lot of people tend to assume performance follows a bell curve, but in some cases, it’s more like a Pareto distribution: the top people do hundreds or thousands of times better than average. Hence, if you eliminate the small fraction of people at the very top, your performance is hosed. Fortunately for VC funds, the startup world is still positive selection.

Less obviously, a world with lots of negative selection might be a nasty one to live in. If you think of yourself as trying to eliminate bad, rather than encourage good, you start operating on the purity vs. contamination moral axis. Any tiny amount of bad, anywhere, must be gotten rid of, and that can lead to all sorts of nastiness. “When you are a Guardian of the Truth, all you can do is try to stave off the inevitable slide into entropy by zapping anything that departs from the Truth.  If there’s some way to pump against entropy, generate new true beliefs along with a little waste heat, that same pump can keep the truth alive without secret police.”

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I asked my father to read this and give his thoughts.

He says that positive selection only works well when you have a very good idea what you need to select for. If you're sending an athlete to the Olympics but the event he'll have to compete in will be chosen at random, you can't just choose the one with the best time on the 800 meter dash, because the event might end up being something like archery, fencing, or weightlifting. And you certainly wouldn't want to send a non-swimmer. If you need a generalist, seeing how well someone does at jumping through a wide variety of arbitrary hoops might really be the best test you can practically implement.

(Now I'm wondering just how good or bad the 800 meter dash actually is at predicting levels of success at unrelated sports. For example, could you tell the difference between an NHL-quality ice hockey player and one that plays on a minor league team just by looking at their times on the 800 meter dash?)

Assuming a significantly large distribution of athletes sent by other rational managers, where all athletes are bound to the same rules of random event selection, I would still send the best possible specialist in a single discipline in this case, because without certainty that all other rational managers know certainly that some generalists will be better in everything than other generalists and that each one is confident that theirs is best, I conclude that some of them attempt a gamble of probabilities and send a specialist, and thus I also send a specialist to maximize my chances of winning.

After all, there are higher chances of the event being my athlete's specialty than there are chances of every single other athlete being less good at it if I pick a generalist, unless the number of possible events is large enough to outweigh the number of athletes. Throw in irrational managers and the possibility of other managers having information unavailable to you, and your father's argument seems very weak.

Now, of course, I'm probably attacking something that wasn't meant to be a strong defensible argument. However, I feel very strongly about the point that negative selection is wrong in many contexts it is currently used in (which I support), as well as the point that positive selection is so difficult and utterly impractical in so many cases (which I want to pound into tiny bits of forgotten wrongness).

I'm not sure where I'm going with this, however. I strongly agree with the article's statements, but my attempts to formulate any further useful thought seem to come up short.

Well, the sports analogy was my own interpretation of what he said.

Game theory question time: you and N other players are playing a dice rolling game. Each player has the choice of rolling a single twenty-sided die, or rolling five four-sided dice. The player with the highest total wins. (Ties are broken by eliminating all non-tying players and then playing again.) Now, rolling 5d4 has an expected score of 12.5 and rolling 1d20 has an expected score of 10.5, so when N=2, it's obviously better to roll 5d4. However, when N becomes sufficiently large, someone is going to roll a 20, so it's better to pick the 20-sided die, which gives you a 1 in 20 chance of rolling a 20 instead of a 1 in 1024 chance of getting five 4s. For exactly what value of N does it become better?

Edit: Fixed stupid math mistakes. That'll teach me to post after staying up all night!

> rolling 1d20 has an expected score of 10 10.5

1 in 256 chance of getting five 4s

4^5 = 2^10 = 1024

One of the most important social structures of modern society is the corporation - a framework for large groups of people to band together and get absolutely huge projects done. In this framework, the structure itself is more important than individual excellence at most levels. To a lesser extent, the same applies to academia and even "society as a whole".

In that context, I think preferring negative selection to positive makes sense: a genius data-entry clerk is less helpful than an insubordinate data-entry clerk is disruptive.

And remember that we have side routes so real geniuses (of some kinds) can still make it: set up their own company, start their own political party, start publishing their work online, design games in their basement, and so on.

And remember that we have side routes so real geniuses (of some kinds) can still make it: set up their own company, start their own political party, start publishing their work online, design games in their basement, and so on.

This is a really good point. It's good to have low barriers to this sort of thing. For instance, if you need to hire a lawyer and an accountant to set up your own company, then a genius cookie baker can't set up their own cookie shop unless they also have the money or connections to get the help of a lawyer and an accountant.

This was my favorite post on your blog and I'm glad you posted it here.

Really good post...it makes a point that is completely new to me, which is always nice.

It does occur to me that the current (negative selection) system would reward "hard work" more, relative to "talent", than a positive selection system. (In quotation marks because those are both metrics that are hard to measure separately from one another.) Someone who is very conscientious and hard-working is likely to compensate for wherever areas they're weaker, in terms of "natural talent", however you define that.

My first, emotional reaction to your post was "I would be screwed in a positive selection system!" As someone who's above average in a lot of areas, not really exceptional in any, and obsessively hard-working enough that it's a running joke among my friends, I like the current system just fine (although I'm not in academia.) I don't know if conscientiousness would have a bigger long-term effect on results than innate brilliance; it probably depends on what field you're talking about.

My intuition says that a positive selection system would probably be a good idea in fields where there is big variance in natural ability, i.e. math or physics, and less so in fields like medicine where a lot of "talent" depends on how willing you are to work hard and keep improving over your whole career.

The concepts of positive and negative selection are not quite well defined in your essay, I think.

Imagine that you have one test, with a gaussian distribution of outcomes. Let's arbitrarily set a threshold, and if people are above this threshold, they have passed this test. Call the sets of passing A and not passing ~A

Would you call this a positive or negative selection? It is neither, in my opinion.

Now, imagine you have two tests, A and B.

A positive test is one where A U B are selected. A negative test is one where ~(~A ^ ~B) are selected.

In other words - the operative difference between positive and negative selection is OR vs. AND.

I've just realized that I have been treating dating as a negative selection process. This might explain the lack of success.

Grades in high school are already like this. To get the best grade from a subject, you need to be good, but not exceptional. So being good but not exceptional in everything brings you the highest possible score.

If instead you are exceptional in a subject or two, and average in a few unrelated subjects, it gives you lower total score, and if the university cared about your grade average, you would have problems getting there, especially if many people with the highest total score competed with you.

Since most production functions are quasiconcave over inputs, negative selection is a cheap method of increasing expected return. You lose some outliers and also people who would be good in those rare domains with quasiconvex production functions, but our system is optimized for the average case.

In the college admissions example, a top school wants to admit undergraduates likely to become successful doctors/lawyers/businesspeople and alumni donors, not gamble that the smart kid with a few Bs in high school is going to revolutionize a scientific field in 15 years. Even if they did, their undergraduate institution would be only the third most important on their CV, after their current institution and where they got their PhD.

This is a good example of individual selection being suboptimal from a group perspective. Each top school would prefer that some other top school gamble on said smart kid, and then if they have the chops for research they can try to grab them when they apply to graduate school or go on the academic job market. Positive selection on undergraduates is just not a smart strategy from an individual institution's perspective since most undergraduates will be going into more conventional fields.

Students at Yale are, for the most part, all strikingly similar – same socioeconomic class, same interests, same pursuits, same life goals, even the same style of dress.

Can I ask on what basis you're drawing this conclusion? I agree with the bulk of what you said about overuse of negative selection, but I challenge the idea that it's producing cookie-cutter student bodies at elite universities. Having attended Yale as an undergrad, your claim strikes me as incorrect, as the Yale student body seemed to me more diverse on all five of those categories than any other (non-online) community I've been a part of -- certainly more so than my high school, my law school, or my current professional environment. That's just my anecdotal experience, so I'm open to the idea that I'm mistaken if you have some more formal analysis to back this up. But this statement jumped out at me as questionable, so I wanted to see where you were getting it from.

I agree with most of it, though the point about academia is a bit contrived.

True, there is a lot of negative selection before you get a cushy job the usual way, but you can certainly bypass quite a few obstacles if you are exceptionally good. For example, solve any of the open problems in math or physics, post a preprint on arxiv.org (well, you may need someone to vouch for you, but that's not really an issue) and you are all set.

Unfortunately, I cannot recall a single discovery in physics in the last half a century that was not made by someone who jumped through the usual hoops. I have met, however, an occasional person who learned grad school-level stuff on their own, but they did not manage to go any farther. My suspicion is therefore that all that negative selection in science, while annoying, does not do a lot of harm compared to potential alternatives. While it filters out some good people, it probably does not reject the very best, otherwise we would see an occasional example of someone making a significant discovery outside academia.

While [negative selection] filters out some good people, it probably does not reject the very best, otherwise we would see an occasional example of someone making a significant discovery outside academia.

I predict that we will indeed see this before too long, now that we have the internet; and it will thus turn out that some of the best people were being filtered out. Access to information and social support/reinforcement is a huge limiting factor.

And of course, if you're willing to look a century back instead of just a half-century, you find the salient example of Einstein -- who didn't even have the internet, but still managed to advance science from outside the "establishment" (which was a sizable apparatus in his time and place, just as it is in ours).

Access to information and social support/reinforcement is a huge limiting factor.

Access to labs, equipment, technicians, funding is an even greater factor. Only mathematicians can really afford to work from home. (And now, computer scientists and computational-xxx people have joined them.)

Unfortunately, I cannot recall a single discovery in physics in the last half a century that was not made by someone who jumped through the usual hoops. I have met, however, an occasional person who learned grad school-level stuff on their own, but they did not manage to go any farther. My suspicion is therefore that all that negative selection in science, while annoying, does not do a lot of harm compared to potential alternatives.

But you don't get to observe any of the discoveries in physics that haven't been made. If a good university education is markedly better for learning physics than autodidactism, then the people who don't jump through the usual hoops will be inhibited by an inferior education and won't be in the position to make discoveries that a person who did jump through those hoops is.

If receiving a high level education and having access to university resources is effectively a precondition for making significant new discoveries in physics today, you would not expect to see people who did not go through the regular procedures making significant new discoveries in physics, even if the negative selection of academia filters out most of the best candidates.