The consequences of school choice

School choice is often heralded as an effective way of combatting inequality in our education system. Proponents argue that competition among schools can help improve or eliminate underperforming schools.

School choice already exists to a certain extent. Private schools are an option for the rich and charter schools are an option for the lucky. There is also homeschooling and some states have other programs. But the vast majority of American children are still educated in regular public schools. This is why I argue, whatever effects school choice may have had so far, its effects if our whole country were to adopt the idea could potentially be strikingly different.

(A quick sidenote for non-U.S. readers: in the U.S. one cannot choose which school they want to attend in primary and secondary public education (with certain, relatively rare exceptions). The school a student has to attend depends on the residence of their family. To sum it up in a very crude way: if one lives in the rich neighborhood, they can attend the school of that neighborhood and vice versa for poor and middle-class people.)

The idea of school choice is something I generally would support. It would indeed allow competition and would let hard-working poor kids attend better schools. But there are certain problems.

Suppose there are two schools in a town and currently there is no school choice. One school serves an upper-middle to upper class neighborhood, the other one serves a lower to middle-class neighborhood. Now let us rate the students’ skill in each school on a scale from 1 to 10. A skill of 10 means that the student is hard-working, smart, talented and could get into the best colleges. A skill of 1 means a student does not care about school, is disruptive, misses and fails classes and is likely to drop out of school before graduating. Then there is everything in between.

What skill a student has of course depends on genetics but as I discussed this in my earlier post, it is influenced by environment to a very large extent. Therefore, it is safe to assume that the “rich” school’s average student will have a larger skill on that 1-10 scale than the “poor” school’s average student. This is just equivalent to saying that children graduating from better high schools are more likely to end up at an Ivy League college, whereas students from worse schools are more likely to not even graduate from high school.

Suppose now that the town votes to introduce school choice. What will happen? Schools will now have to have admissions procedures. It is quite likely that any student from the poor school district whose skill is somewhat above the skill of worst students in the rich district will be admitted to the rich school. But this would mean that the rich school will have to drop its worst students who will now have to go to the poor school.

It’s quite clear to see what will happen: the rich school’s average skill is going to grow, the poor school’s is going to decrease. To see this, consider an example of two schools with 20 students:

School choice, inequality and polarization

You can see that there are 20 students in each school and their skills go from 1 to 10. The average skill in the poor school is 5.5, in the rich school it’s 7.0. Now let us assume that every single year, this is the skillset of new students. And that every year the best student from the poor district applies to and gets into the rich school, while the rich school drops its worst student in order to accomodate the new student. An equivalent assumption is that one student from each school can transfer. Then the top student from the poor school will be able to get into the rich school. The rich school will then “expel” the worst student to make room. The worst student will continue studying in the poor school.

To iterate this process, consider the following code in Python (school 1 = poor, school 2 = rich):

for i in range(10):
    one_to_two = school1.pop(school1.index(max(school1)))
    two_to_one = school2.pop(school2.index(min(school2)))

    school1.append(two_to_one)
    school2.append(one_to_two)

The results after 10 iterations is that the poor school’s average drops to 4.6, while the rich school’s increases to 7.9. This increases the initial gap of 1.5 skill points to 3.3. The gap gradually widens. One can equally think of this model as a situation in which students from the poor district are gradually discovering the opportunities the rich district provides. As more and more students go study there, the gap between the two schools widens until it reaches a stable allocation.

School choice, inequality and polarization, graph

This model, which is quite reasonable in my opinion, basically concludes that if we introduce school choice universally, then good students who currently have to attend bad schools will flock to good schools. But then the worst students of these good schools will be forced out to make room for these new students. They will then have to attend the worse schools. This is quite meritocratic but it will potentially lead to an even larger polarization of our school system.

One may argue that our system is already polarized. In that case, school choice wouldn’t worsen the situation because it couldn’t. But obviously, it wouldn’t improve it, either.

We could also consider accepting this divergence and saying that less bright students need different learning methods anyway. If we can fund worse schools adequately, this segregation may even be beneficial. This is something that I am pretty sure is much discussed in the literature and since I am not familiar with it I will not get into it. Let me just note that a very significant amount of (probably the vast majority of) students have low skill levels because of their environment and not because of their innate inferiority. This means that what they need is not different learning methods. Therefore, keeping them in schools where they are treated as having learning difficulties will most certainly not help. They need change in their environment, which is a lot more complex issue.

So what is the conclusion of all of this? It is that universally introduced unregulated school choice will weakly increase (i.e. will not decrease but might increase) the divergence and polarization of our public schools. The question is to what extent we are ready to accept this. If there are no frictions, this is a completely meritocratic system. The opposite could be standardizing all schools and then using a lottery system to allocate places among students. This would pretty much make all schools homogeneous and would be completely egalitarian. But it could be tweaked. We could say if a student fulfills certain criteria, then they can specifiy a limited number of schools for which they want to be considered in the lottery. We could struck a balance there somewhere.

The options between the two extremes are limitless depending on what society wants. Therefore, it is time to decide and get rid of our current system because that one is neither meritocratic nor egalitarian. It is just plain terrible.

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