The Atlantic’s Julie Halpert asks us to imagine two scenarios. In one, “every child would have to attend private school, and in the other, every child would have to attend public school. Which scenario would be more likely to improve or worsen kids’ educational outcomes—and, by extension, the health of American society?”

She quotes me a few times with doubts about an all-private system:

Levine’s prediction for an all-private-school world? “You’ll have this very intensely competitive market in which every child would be assessed,” he said, “and if your child has behavioral issues, they won’t get as good a deal in the market.” … An all-private-school world, then, would foster a system that thrives on selectivity. As Levine emphasized, private schools can’t just scale up like companies can because small size is often a selling point in K-12 education; the best schools are those that don’t accept large numbers of students.

I am not a doctrinaire opponent of choice or market mechanisms in education. Denmark is rightly admired as a model social welfare system, yet 15.6% of Danish kids attend private schools fully funded by vouchers. In many European cities, all the schools are what we would call “charters”: basically self-governing entities, regulated by the state, that get public money in proportion to their enrollments. (Rural areas tend to offer less choice, simply because the low population density favors local mandatory-enrollment schools).

By the way, the Danish Union of Teachers represents 97% of primary and secondary teachers. A competitive market with high union density may offer a good combination of choice plus job security.

Meanwhile, it’s not so clear that offering only public schools really gets rid of market competition. The American “common school” model–one school system for all the children in each political jurisdiction–reflects a fierce market for housing. Americans of means choose their residence in order to determine their kids’ schools. It would arguably be better to separate the market for schools from the market for houses, rather than combining them and kidding ourselves that we have ever had a “public” school system.

But I was asked whether I’d like to see a system without public schools at all–Milton Friedman’s model of vouchers for an all-private system. I offered several ways in which education differs from other markets.

One difference is that education is meant to produce public goods, such as a unified body of informed citizens, not just private goods, such as each graduate’s value in the labor market. I agree with this normative position, but the empirical evidence is complicated. There is evidence that Catholic high schools in the United States–which are private–have done a better job than public schools of generating public goods.

Another difference is that educators typically do not want to increase the size of their own enterprise. For teachers, it’s better to have 18 rather than 8o students. For principals, it may be preferable to have 20 rather than 200 teachers. Families may also prefer smaller and more selective schools. The usual incentives to “scale up” don’t apply.

A third difference is that kids, not just schools, have unequal market value. Coca-Cola doesn’t care who you are if you have enough money for a bottle of Coke. Detroit Country Day School (the institution that Halpert uses as an example) definitely does care who you are if you want to enroll. The other kids contribute profoundly to each student’s experience and trajectory.

In fact, I have sometimes wondered whether a university that had sufficient status–thanks to its history and branding–could offer no education at all, and its students would still fare well thanks to their cultural capital, the network ties they form among their peers, and the market signal conveyed by enrolling them. The admissions office and the dormitories could do the whole job of conveying social advantage. It would not be irrational to prefer (and to pay tuition for) such an institution rather than an open-access university that added more value in the classroom.

In the long run, it might be a mistake to blatantly offer no pedagogy or curriculum whatsoever. That might erode an institution’s brand. However, I’m confident that many highly selective schools and colleges do a subtly worse job of instruction than many low-status institutions that enroll less advantaged kids. The former still win in the market for students because they have already attracted other privileged students.

Charging higher tuition can even make a school more desirable by ensuring that most of its students have high social positions. (A school may then get even more value by admitting a few non-privileged kids for “diversity,” charging them less than the sticker price).

These are not reasons to reject choice and market mechanisms altogether, but they do suggest that facile analogies between ordinary consumer markets and education are likely to mislead.