
Why a Dutch court stopped high school students from swapping schools (2017) - m4lvin
https://medium.com/social-choice/why-a-dutch-court-stopped-high-school-students-from-exchanging-schools-1315303a48b6
======
elygre
As a European exchange student, I took a sociology class as a senior in a US
high school. Our teacher ran an experiment with "money", where those with lots
of "money" were allowed to change the rules for each round, creating an unfair
playing ground favoring the rich.

I objected to the game and the rules, and did not want to play. After the
game, in class, he commented that "Exchange students always object that the
rules are unfair, while local students always accept that the rich get to set
them."

Without even knowing where people are from, I sense a similar trend in this
discussion: Europeans are more willing (trained and socialized) to sacrifice
individual preferences in favor of the "greater good".

(Your mileage will vary. Not exact science. Not science at all. Just a
feeling.)

(Edit: Spelling)

~~~
aianus
Surely the Netherlands has private schools?

I don't think the rich are sacrificing anything by this lottery. Some middle-
class kids might have to go to a worse school to allow some poor kids to go to
a better school but the rich are unaffected.

~~~
lumberjack
No. The rich and everyone else send their kids to the same public schools.

In the Netherlands people value the idea of living in a classless society. It
would not be acceptable for certain people to have their own "special" schools
where their kids get "special" education.

The way the rich try to get around that is by congregating in the same rich
neighbourhoods and sending their kids to the same school. That is why the
lottery exists, to distribute the kids evenly in a fair manner.

~~~
vostok
> No. The rich and everyone else send their kids to the same public schools.

They don't send their kids to boarding schools in the UK/US/Switzerland?

~~~
StudentStuff
Sure, but is such a school giving their child any actual advantage? They'll be
in a foreign country taught by likely a lower quality teacher (esp. in US
private schools, there is a reason our private teachers make $10k less a
year).

~~~
ghaff
If they want to work in the US/UK/Switzerland? Or perhaps internationally more
broadly? Probably. And I wouldn’t assume those private schools and their
environment are giving a lower quality education.

~~~
Tijdreiziger
There are a lot of schools with bilingual programs (English+Dutch) and the
programs are of high quality. Seems simpler to go for such a program, no need
to send your kid abroad.

------
mabbo
I wonder if the Gale–Shapley algorithm[0] would work in this situation.

That algorithm applies to the stable marriage problem: N men and N women need
to be paired such that no two members in each set would both prefer to be with
each other over their partners.

The algorithm has each person rank every member of the opposite gender in
preferential order. Then, one side (let's presume the women) take turns
picking from the other in order of their preferences. If the woman A's top
choice is man X, but man X is already taken by woman B, then he will swap iff
he prefers woman A over woman B. If he prefers woman B over woman A, then
woman A moves down to her next choice in the list. If you follow this pattern
to conclusion, everyone is paired and there will not exist a man and woman who
both want to be with each other more than their current partners.

We could apply this to school selection. Every student ranks all schools from
most to least preferred. All schools then 'rank' students via any criteria
they want. Want to put students with siblings in the school ahead of all
others? Easily done. For any equally-preferred students, sort randomly. The
"women" translates to students, and the "men" translates to "spot in this
school".

Might not stop strategizing, but it's a great way to handle pairings with
preferences involved.

[0][https://en.wikipedia.org/wiki/Stable_marriage_problem#Soluti...](https://en.wikipedia.org/wiki/Stable_marriage_problem#Solution)

~~~
niftich
In the US, this algorithm is used to place medical graduates at teaching
hospitals, by the National Resident Matching Program. And of course, college
admissions was the topic of Gale and Shapley's 1962 paper, 'College Admissions
and the Stability of Marriage' which publicized the algorithm [1].

[1] [https://doi.org/10.2307%2F2312726](https://doi.org/10.2307%2F2312726)

------
nemetroid
To elaborate on the example in the article, the main reason that swapping is
disallowed is that by necessity, there exists a third student which is screwed
by the swap.

The deferred acceptance algorithm always creates a stable matching, which
means that it does not contain any blocking pairs. A blocking pair is a pair
<student, school> where the student is not assigned to the school, but prefers
the school to their current assignment, and the school prefers the student
above their worst ranked admitted student.

When executed as described in the article, the algorithm produces a student-
optimal solution, which means that for all students, _no other stable matching
exists where the student is better off_.

In the example, where student a preferred school A over B (their current
assignment) and student b preferred school B over A (their current
assignment), both students would become better off by swapping. Thus, the
matching produced after swapping cannot be stable: there must exist some
student x who now forms a blocking pair together with either school A or B.

To explain how this happens:

Say that student a is the first to select schools (the iteration order of the
students does not matter for the end result, this just makes the steps a bit
clearer). Then, at the start, we have this assignment:

A: a

Since a is not assigned to A in the final solution, at some point a has worse
rank than all students assigned to A and is pushed out:

A: x, y, z (say that the capacity of A is three)

This means that A ranks x, y and z higher than a. If any subsequent students
push out x, y or z, they too will have higher rank than a.

At some point b is then assigned to A. This means that b has higher rank than
x, y and z. At least one of them, say x, has been pushed out by now.

If a and b were allowed to swap, then <x, A> would form a blocking pair since
x prefers A to their current assignment, and A prefers x to their lowest
ranked admitted student (a). Thus the solution would no longer be stable.

~~~
eridius
I'm confused, why must b push one of x, y, or z out? Why isn't one of x, y, or
z _already_ b? Or to put it another way, why can't a be the most-preferred
non-accepted student for A?

~~~
nemetroid
You are right, I forgot to state an assumption, which is that "a gets pushed
out of A" happens before "b gets pushed out of B" (and then goes on to apply
to A).

One of those things must happen before the other (each step in the algorithm
is a currently-unassigned student applying to their next choice). In your
case, if a is the most-preferred non-accepted student for A, then b must have
been pushed out of B first, so the argument applies to B instead.

------
ericpts
What would be a good reason for distributing students based on luck (which is
what I gathered from the article), versus having everyone take a standardized
test and then assigning pupils to schools based on their performance in their
test?

The test approach seems the fairest to me, as a grade A student should have a
higher priority of getting into a top school than a lower grade student.

Contrast this with having a high achieving student not getting into the school
of his choice due to sheer bad luck, and I do not see much benefit from the
lottery system.

~~~
evoloution
There has been a shift in conversation over the last years and at least in US
they are claiming that the highest variance in student performance can be
attributed to socioeconomic status and developmental environment. So it would
seem like selecting based on school performance could make things worse. One
could make the case that this would really hurt very smart/ high-performing
individuals from low socio-economic status families but most people (and
rational policy) care about helping/ making an impact at the population level.

~~~
Spooky23
That’s what people say, because it’s hard to say anything else without hitting
narratives that will be interpreted as racist or insensitive for other
reasons.

Household culture is a big predictor of outcome. Parental age is another.
Asian/Indian kids buck the bigger trend, because those family cultures value
education as _the_ way to advance.

Usually these policy discussions get dumbed down into inner-city vs suburbia
comparison. But I think we’re starting to see bigger cohorts of white kids
from suburban professional backgrounds who are not doing better than their
parents.

------
nightcracker
TL;DR: students are not allowed to swap because (in the current system) that
would enable strategizing. It encourages people to list popular schools rather
than their preferred choices for the lottery, and then trade their popular
spot for their true preferences afterwards.

The system has been designed to not allow strategizing, as strategy often
backfires on the student, as well as it's argued that students from lower
class backgrounds make more strategic mistakes.

A nitpick from me on the article though:

> Designing a lottery system to place students at the different schools is not
> just a mathematical optimization problem. Different design choices can have
> far-reaching effects. On whether everyone gets equal opportunities, for
> example.

It absolutely is. It's called game theory. And 'no strategizing' is a
criterion you can optimize for.

This has close relations to the well-known stable marriage problem. The
seminal paper on both these problems is Gale and Shapley, College Admissions
and the Stability of Marriage.

~~~
closeparen
So it ensures that unequal outcomes are always the result of random chance,
and never the result of a skill gap. That seems exactly backwards: you would
want egalitarian policy to minimize random factors like your parents’ wealth
so that factors like the student’s own skills dominate. Can anyone elaborate?

~~~
Barrin92
the ability of a student to strategize is strongly correlated to the education
and wealth of the parents. (as pointed out in the post).

the discrepancy in strategic aptitude is itself a result of chance. Only
through this absolute form of randomness, you are actually eliminating the
wealth, education and aptitude bonus of upper-class households.

Your comment is a nice signifier of the difference in American and Dutch
culture. Dutch people don't buy the idea that individual strategizing is going
to advantage the interests of lower-class students, because they recognise
that lower class students are already disadvantaged when they enter the
system.

------
rufusroflpunch
Why not go one step further and randomize the teaching pool? Just tell
teachers where they can and can't work, just to make sure that all students
get a shot at the best teachers.

What isn't justifiable in the name of fairness?

~~~
Tijdreiziger
That actually seems like quite a good proposal. If a teacher applies to a
school in a certain part of a city, presumably they'd also be happy to work at
any other school in that part of the city. It would also be a win for the
teachers, because they'd only have to apply once for multiple schools.

~~~
kalleboo
In Japan they actually do shuffle teachers around the school district every
couple of years.

------
csense
Fascinating article.

The obvious research question: Is there an assignment system where the best
strategy is to list your true preferences, _and_ is Pareto efficient (no
win/win trading of assignment is possible)?

What's wrong with simply randomizing the list of students, then walking the
randomized list and giving each student his/her highest-ranked school that
hasn't yet been filled by the assignment of students higher on the list?

Does some variant of Arrow's impossibility theorem [1] apply to this
situation?

It might also shed light on the causes and dynamics of poverty to figure out
the exact causal mechanism by which "students from poorer neighborhoods make
more strategic mistakes."

Is poor strategic decision-making ability a _cause_ of poverty (the poor are
poor because they don't make smart strategic decisions about money and life
choices)? Or is it an _effect_ of poverty (having a single parent or parents
working multiple jobs means less intellectual stimulation and help with
homework, not being able to afford nutritious food or have time to cook it
causes poor nutrition which affects brain development, etc., which leads to
lower general intelligence and strategic thinking ability)?

[1]
[https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...](https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem)

~~~
gowld
> "students from poorer neighborhoods make more strategic mistakes."

It's likely simpler than you guess, and not because poorer people are dumber
(I'm not even sure why you assumed that making strategic mistakes in college
planning is caused by low intelligence): students in poorer neighborhoods
aren't plugged into the privilege networks, that tell them which are the best
schools to apply to.

~~~
Scarblac
But having wrong preferences in the first place isn't the kind of strategic
mistake they're talking about.

It's thinking of the type "my 1st preference is school A, but I probably won't
get in, so I'll say my preference is B so that I get that at least" in cases
where they would have got into A if they had stated it as their #1.

------
danielvf
While this isn't a surprising tradeoff for the Netherlands, what does surprise
me is the size of the tradeoff they are willing to make. Almost eight percent
of the entire student body would be going to a not-first choice school as a
result of stopping the trades. (Using the numbers in the article) That's quite
a hit.

There are approximately 8,000 students per year entering Amsterdam high
schools. According to the article, in 2015 when the new lottery system was
introduced, 600 students would be able to attend their top choice school by
swapping with someone else after the lottery.

~~~
fmihaila
> While this isn't a surprising tradeoff for the Netherlands, what does
> surprise me is the size of the tradeoff they are willing to make. Almost
> eight percent of the entire student body would be going to a not-first
> choice school as a result. (Using the numbers in the article) That's quite a
> hit.

It is, but it needs to be balanced against the percentage of disappointed
students in a regular, non-lottery system. The article doesn’t say what that
is, unfortunately.

~~~
danielvf
It's certainly true that the current state is better than a non-lottery
system. That's not what the judge's decision changed though - it changed from
preference+lottery with trades to preference+lottery without trades.

This creates a strictly worse outcome for that school year, since only
students who would mutually benefit from a trade would trade, and students who
did nothing or could not trade would remain unchanged.

~~~
fmihaila
> This creates a strictly worse outcome for that school year, since only
> students who would mutually benefit from a trade would trade, and students
> who did nothing or could not trade would remain unchanged.

That's true. My understanding is that they did that for two reasons. The first
was that a property of this particular algorithm is that mutually beneficial
swaps are only possible if there is a third student placed at a third school
who would also prefer one of the two being swapped, but whose school is not
desirable, so he doesn't have a choice, which was deemed unfair (I don't know
how I feel about this argument). The second was that allowing trades for this
school year would encourage strategizing in the following years, which would
lead to worse outcomes over time. These two things were addressed when they
changed the lottery system once again.

------
GreeniFi
This is really interesting - thanks for posting. What strikes me is that a
court ruling implicitly took a view on the meaning of “fairness”. But fairness
is a deeply subjective concept, something courts in a lot of countries would
avoid going anywhere near! What’s interesting is that concepts of fairness
vary greatly across cultures - and it makes me wonder how in multi-cultural,
multi-ethnic Europe we will arrive at newly-agreed definitions of fairness and
what that will be.

~~~
riquito
Fairness in statistic is not not a subjective concept, it's a property of an
algorithm.

~~~
Thiez
Fairness is absolutely a subjective concept. E.g. in the context of school
choice, which is fair? Let's say there are 20 students applying to a school,
and there are 10 spots available.

a) All students applying to the school have the same chance to get a spot: 50%

b) The best 10 students (by some definition of 'best', e.g. grades or an entry
exam) get in.

c) The 10 students with the richest parents get in.

d) The 10 students that live closest to the school get in.

We could go further: when 15 of the applicants are boys and 5 are girls (or
vice versa), wouldn't it be more fair when 5 of each are chosen? How about
racial distributions?

Ultimately how you define fairness _is_ subjective. Obviously once you have
defined fairness you can attempt to measure it using mathematics / statistics.

~~~
zwily
The person you responded explicitly said “fairness in statistics”.

~~~
Thiez
What does "fairness in statistics" even mean? Perhaps there is a very obvious
definition that I don't know about? Would you please define it for me, and (if
this is non-obvious) explain how it relates to the school choice problem?

------
m4lvin
For details about the voting algorithms, alternative methods based on genetic
optimisation and Haskell implementations, have a look at the the MSc thesis
"Genetic-Algorithmic Optimisation for School-Allocation Mechanisms - A Study
of Amsterdam’s Student to High-School Allocation Problem" by Philip W.B.
Michgelsen:
[https://eprints.illc.uva.nl/982/1/MoL-2016-10.text.pdf](https://eprints.illc.uva.nl/982/1/MoL-2016-10.text.pdf)

------
Illniyar
I don't see why strategizing is a problem. Rather then ban it, encourage it,
everyone should make the best strategy. Once everyone does, I think it will
become clear that the best strategy is to choose the schools you want.

------
jotadambalakiri
> In fact, whenever two students win each other’s jackpot trade, there must
> always be a third student that’s higher on the ranking at one of the schools
> — and that wants a spot at this school

I don't think that's true, what if in both schools they were ranked last place
and last place plus one?

~~~
pfedak
The algorithm won't assign them that way in that case. A more thorough
explanation is elsewhere in the comments, but essentially if Alice got placed
at B despite preferring A, they had to have gotten bumped from A, then bumped
someone (or found an open space) at B. But Bob can't have been the person that
bumped them: if there was an open space at B, Bob would never even have
considered A; if Alice bumped someone at school B, then in your situation it
must have been Bob, and so for Bob to end up at A when Alice couldn't there
had to be someone else with priority between Alice and Bob for A, exactly the
person getting screwed over by the swap.

------
rukittenme
Optimizing for fairness is antithetical to human rights. More people would be
better off if you allowed swapping. But because some people would not be
better off they don't allow it for anyone.

~~~
gpvos
_> More people would be better off if you allowed swapping._

Please give a worked-out example, based on a watertight definition of "better
off".

 _> But because some people would not be better off they don't allow it for
anyone._

As far as I understand, the system is now set up so that if they allowed it,
and taking human behaviour into account, overall more people would be worse
off than better off.

~~~
michaelcampbell
Please show how the current system is better than what he proposed, based on a
watertight definition of "better off".

You've proposed a constraint that can't realistically be achieved.

------
himom
At least they had some choice. Growing up, I had no choice and couldn’t go to
an elementary school a block from my house because of race quotas and forced
busing to a magnet school to improve their stats. 1.5 hours each way, 3 hours
total each school day. I was up at 4:50a. I thank the social justice warriors
whom used more discrimination instead of equity to ostensibly make things
“better.” (Equity is fairer and more advantageous than equality because it’s
customized and resourced equally, instead of one-sized-fits-some.)

------
overdrivetg
For some reason I am able to understand single-DA better as:

1\. All students are sequentially ranked via lottery

2\. You walk down the list, and each student gets their pick of schools with
remaining spaces open

Side note, but it also seems IMO that "fairness" could improve if your lottery
position is impacted by your past academic performance. Then the better
student you have been, the more chance you have of being higher in the lottery
order to select a school.

And similar in the debate over which voting system is best, there is also
something to be said for preferring that the system being used is easily
understandable and feeling fair to the individual, even in the case where it
is (slightly) less fair in the aggregate.

Then you have the added bonus of fewer annoyed parents suing you, and only the
mathematician parents will complain =)

And then if you also add in the idea of academic performance playing a role,
parents can rationalize their situation as having been under their control all
along - if their child had performed better, they would have had the ability
to choose earlier in the list.

Of course, this is all assuming you believe that grades should convey some
preferential status. But if you don't believe that, then why have grades at
all?

------
jupp0r
Is it only me, or is denying gifted children good education based on pure luck
unfair in the first place?

~~~
eloisant
They're not denying gifted children good education.

They're giving good education to everyone, and don't reserve the best to the
students who are doing well already and will succeed anyway.

------
topkai22
This does beg the question: why aren’t the popular schools expanding to meet
demand? My guess from other comments is that the center city location is often
the driving reason for the pick, so the cost of acquiring similar real estate
is prohibitive (also meaning that the the students selected for those schools
are “unfairly” enjoying a high imputed income by enjoying that location)

An interesting feature of the US charter school system in my area is that
because their funding is directly tied to headcount (I believe there is bonus
money for special ed students too), they are typically always looking at how
to expand. Each school runs its own lottery, and being over-subscribed is
looked at as a signal they need to expand their offerings.

------
49bc
Reminds me of something predicted in “Weapons or Math Destructive” an opique
algorithm deciding our fate that’s difficult (impossible?) to fully audit.
It’s a cruel fate we’re leaving ourselves too if we don’t leave _a lot_ of
room for common sense.

------
Ice_cream_suit
"Almost 70 percent of schools in the Netherlands are administered by private
school boards, and all schools are government funded equally.

The instrumental variables results show that private school attendance is
associated with higher test scores. Private school size effects in math,
reading and science achievement are 0.19, 0.31 and 0.21"

[http://documents.worldbank.org/curated/en/705501468323653171...](http://documents.worldbank.org/curated/en/705501468323653171/Private-
education-provision-and-public-finance-the-Netherlands)

------
fallingfrog
It's really weird to see the Dutch authorities using math to determine which
system is better; it's even more bizarre to see them caring about fairness.
Here in the states such an approach would be unthinkable. Whoever had the most
money would get their way, and any kind of math is viewed as tricksy confusing
lefty crap.

------
closeparen
The intuition that lotteries are substantially more fair than markets is a
strange one. There are already lotteries that redistribute money. If we accept
that random windfalls are the right way to allocate resources, why is it
preferably to hand out million-dollar discounts on condos or school slots that
confer millions-dollar lifetime earning bumps vs. simply writing million
dollar checks? The check winner has strictly more options than the condo
owner, who is deed-restricted on resale, or the school slot winner, who might
prefer to retire early instead.

Lotteries get around unequal capability to spend, but so does the right tax
policy or even an alternate currency scheme where you get non-tradable points
to allocate across the various socialized axes of life. In a system with
several independent lotteries, it’s possible to lose all of them, win the ones
you don’t care about and lose the ones you do, or win them all. Allocating
money gets you a kind of conservation effect: maybe you don’t care about
school, so you got a nice house instead. Maybe the opposite. But with roughly
the same spending capacity as everyone else, you definitely won’t win or lose
big on all axes at once, and can make tradeoffs to win when it’s more
important to you.

------
fouc
>The central point is that efficiency and fairness were in conflict. Allowing
trading would make the outcome a bit more efficient: some students would get a
better outcome. But it would come at a price. The price is that the system
would be less fair.

Wow. It never occurred to me before that efficiency could create unfairness.

~~~
Terr_
Is that sarcasm? I mean, the most "efficient" algorithm for distributing
surplus money to citizens' bank-accounts would be to transfer the entire sum
into the first person you see..

------
nickpp
"Spread the unhappiness as equally as possible."

This could be Socialism's new motto!

------
shagie
From 9 months ago...
[https://news.ycombinator.com/item?id=15062125](https://news.ycombinator.com/item?id=15062125)

~~~
m4lvin
Oops, sorry. I did check whether this had been posted before, but missed the
old entry because the article URL changed...

[https://hn.algolia.com/?query=https:%2F%2Fmedium.com%2Fpopul...](https://hn.algolia.com/?query=https:%2F%2Fmedium.com%2Fpopular-
choice)

[https://hn.algolia.com/?query=https:%2F%2Fmedium.com%2Fsocia...](https://hn.algolia.com/?query=https:%2F%2Fmedium.com%2Fsocial-
choice)

~~~
shagie
No worries. It’s interesting seeing new discussions about it and how the
points line up with older discussions.

------
blockpress
And another reason to avoid the public "education" system.

They will make you pay (via taxes) for services you do not want or need.... to
enroll at a place you do not want to be.

How lovely.

~~~
IkmoIkmo
That's not quite right.

We're talking about a fundamental shortage of capacity for popular schools
here. i.e. there are 10k spots and 8k students, but the top schools have fewer
spots than interested students.

A private system wouldn't solve this problem. It'd only allow profit-seeking
schools to admit the richest students only. It's not a recipe for societal
success because you're giving children a ticket not based on merit, but based
on their parents' riches. This is closer to a plutocracy than a meritocracy.
But either way, merit is hard to define because we're talking about 11 year
old kids deciding on secondary school in the Netherlands starting around age
12.

So you need some way of ranking students. The first one is student preference.
It's not the case that you get enrolled at a school you had no interest in.
The vast majority of students are enrolled in their schools of choice, but
some of them may need to accept their 2nd or 3rd choice. In any case, the game
theoretically driven choice affords students the highest chance of getting
into a school closest to their preference.

The Dutch public school system does quite well and has good outcomes, a
testament to how few private schools there are despite private schools being
given ample room to thrive here.

~~~
StudentStuff
> The Dutch public school system does quite well and has good outcomes, a
> testament to how few private schools there are despite private schools being
> given ample room to thrive here.

I beg to differ, there is not ample room for private schools to thrive. This
is primarily due to higher social cohesion as compared to other countries, the
social acceptance of sending your kid to a private school in the US is
generally assumed, whereas one is apt to be looked down on if they choose to
have their children go to a less resourced, private school in the Netherlands.

Despite private schools here in the US providing students with a lower quality
teacher (here in Seattle, they pay $10k less a year to private school teachers
than the school district does on average), while also permitting students to
spread disease and not vaccinate, many upper class and middle class families
send their kids to these schools. Its a testament to a lack of information and
push back against objectively shitty schools.

On the topic of vaccines, its crazy that the Catholic Church allows kids in
their private schools to not be vaccinated. They're single handedly bringing
back diseases that hadn't been a notable issue in decades.

~~~
IkmoIkmo
> whereas one is apt to be looked down on if they choose to have their
> children go to a less resourced, private school in the Netherlands.

I'm not sure that's true. Private schools are typically well-resourced in the
Netherlands. For example, international schools tend to charge about 20k per
academic year whereas public schools make do with 8.5k per year. Quality isn't
bad in private schools here, it's quite good actually. But so is the public
system which has socialised costs. Most parents are quite content with this
system.

