> Pushing troublesome kids out isn't gaming the system in the same sense that fudging exam results is, because it makes the school better for all the remaining kids. (I think "gaming the system" should be reserved for things that are overall zero- or negative-sum.)

The troublesome kid goes somewhere, very likely somewhere worse equipped to deal with troublesome kids, not being a fancy school with a ton of money and all.

That's the bad design of the system, that a kid that predictably will ruin learning experience of all their classmates, has no place to go where they would cause least harm.

The system simply denies existence of such kids, and pretends that teachers just need to work harder, or we need to throw more money on that kid, and then everything will magically be ok.

What's positive sum for the school might be negative sum for the whole school system, or for the whole of society, depending on where the troublemakers end up. Are they sent to a special school with lower class sizes and more oversight, do they just end up at another school down the road, or are they thrown out into a society they're not prepared to deal with?

I claim it's positive sum for society. To be concrete, suppose that moving the troublemakingest 5% out of a school lets the remaining 95% of kids learn 20% more. And the 5% learn about the same. So overall society is up 20% * 95% = 19%.

It depends on the numbers, of course. If the 95% of kids only learned 1% more, it wouldn't be worth it.

It's notoriously hard to measure those numbers because everything is confounded by everything else and experiments take decades to run. But I think 20% is plausible and 1% isn't.

You're only looking at the gained education for the 95% and the lost education for the 5%, not at the social cost of some of the already disengaged 5% ending up in jail for armed robbery or murder.

Again, it all depends on where the 5% end up. You're not allowed to take them out back and shoot them like an aggressive dog, so are you going to look after them and give them some kind of a future, or are you going to throw kids out onto the street to grow up into career criminals?

Those numbers are made up to support your assumptions. I claim the troublemakingest 5% have an increased chance of having an outsized negative effect on overall society, and by tossing them by their ears, we double their chances of behaviors that have serious (10X) negative effects: perpetrating fraud, abuse, or violence.

Depending on assumptions, it is easy to argue that money is best spent accelerating our brightest minds and giving extra support for the most at-risk, letting the middle atrophy. Or it is best to treat everyone equally, which certainly leaves the top underfulfilled and the bottom underprepared. It's just spitballing.

Aren't you talking past the accusation? It isn't just troublemakers that were pushed out. Low scoring students will be, too.

Are we talking about trouble making kids, or kids who aren't going to ace their exams?

Your numbers are all invented whole cloth; please don't try to math with them.

More precisely: Why should I believe that the remaining kids learn more? In my experience, everyone learns more when they teach, as it forces them to shore up their assumptions. (When you learn something yourself, you learn one wrong way to do it. When you teach, you learn thirty wrong ways.) Having kids who think differently around for peer exchange is then a good thing overall. The struggling kids have stronger peers around to teach them, and the stronger kids have more chances to teach.