> Two people engaging in consensual trade would be better off by the definition of trade.
Not if their swap implicitly makes everyone else worse off though; and this is precisely the claim that judges make, that you cannot simply isolate the effects of the swap without considering the global consequences of the state of the 'game', so to speak.
Again, please be specific. You trade places with someone else. Now you're on your preferred school and so is the person you traded with. I wasn't able to trade, therefore I'm in the school I was assigned by the lottery.
My situation is exactly the same whether you traded your place or not. How can it possibly be worse?
And the global consequences, which seem to be the main concern here, has clearly improved, as more people are happier in their preferred schools.
OK, we'll talk about your specific example and not globally.
Suppose that Alice inherently belongs to some identifiable Group A — based on IQ, artistic- or athletic ability, ethnicity, whatever — but she gets randomly assigned to a school where the majority of students belong to Group B. It's the other way around for Bob, who inherently belongs to Group B but is randomly assigned to a school where the majority of students belong to Group A.
Now suppose that Alice and Bob would each rather be in schools in which the majority consisted of "their own kind." And imagine that there are, say, 50,000 Alices and Bobs in the school district.
In that situation, allowing Alices and Bobs to swap schools at will could easily result in self-sorting that might legitimately be disfavored by the school district, the state government, etc. For example, the school district might well legitimately want students to experience school with a cross-section of students from other groups, not just with "their own kind."
Well honestly this example isn’t very convincing. If some bureaucrat thinks children should go to this or that school, we should do it because...?
Would you prevent Alice and Bob from experiencing schools that are perfect matches for their abilities? Shouldn’t this be their or their parents’ call?
Why not go to the actual example from the article, which is that if you allow trading, then you will encourage strategic behavior from parents in picking schools in future rounds.
People who don't engage in strategic ranking will on average be worse off than they were before.
If all people engage in strategic ranking, then it essentially imposes the 'search cost' of gaming the system optimally on all participants; this search cost may be much greater than the local benefit of swaps.
Also, some parents (e.g. the locals, the wealthy and connected) may be much better at doing strategic ranking then other parents, so it may inherently advantages certain groups over others.
I think there is legitimate debate over whether the local benefits to the few are more important than global objectives, but denying that there are shared objectives (e.g. 'fairness' and de-escalating local competition) that sometimes demand local sacrifices is silly.
I would be individually better off if I didn't have to pay taxes and not receive services, and yet we all recognize that if everyone could individually opt out of taxes, then the entire system would probably collapse.
And don't tell me that I had the rational choice to pay taxes: my tax obligation was put on me because of my citizenship and birth, which I did not enter in out of my free will.
I wrote about this elsewhere in the thread. You can make this pout about strategizing in future lotteries, but this doesn’t seem to be what happened at all in this specific instance. A more reasonable decision then would have been to allow the exchange, even if just this one time.
You should also consider that if we got each others’ best preference, this is a sign of a broken system, because we could have clearly been assigned to our first choices in the first place. So in my view, the exchange should be allowed, and then the system fixed so that such situations are not possible.
> People who don't engage in strategic ranking will on average be worse off than they were before.
How? They will be in the same school regardless of other students switching or not. And even if you didn’t strategize, you might receive an offer for an exchange, so you could even end up just as well as someone who did strategize.
I don’t get where this idea that globally the students will be better off if exchanging places is forbidden. Some people will be better off by exchanging, others will be in the same position as they were before. It’s clear that globally the system will have gained from more people being at their preferred schools.
Your tax example doesn’t apply, because obviously if I stop paying taxes there will be less government resources available to get things done (although we could discuss whether giving money to the government is actually a good way to get things done). Switching schools is different because it only affects the two people involved.
Thanks for taking the time to reply in depth. I think this is a situation with a bit of nuance, and it's possible to really endlessly argue about the issue if we don't tie down the definitions a bit.
> You should also consider that if we got each others’ best preference, this is a sign of a broken system, because we could have clearly been assigned to our first choices in the first place. So in my view, the exchange should be allowed, and then the system fixed so that such situations are not possible.
The thing is that matching systems have been studied for a long time and there is a very rich game theoretic literature that studies this both from a pure theory perspective (where we assume people's preferences are given), and also in real life (e.g. the doctor matching system in the US).
What you're demanding here is that the matching system is finds a stable matching, such that there are no trades that any pair of players would be willing to make.
This is an actual goal of most matching systems. The problem is that it conflicts with the goal of relieving participants from making strategizing choices[1] [2].
Not to get into the weeds to much, but you can see that in the classical stable marriage problem, where only men propose and women either accept or reject, the matching is only stable amongst the men: no man would be willing to switch his partner with another man, but there will (in general) be women who are willing to switch her partner with another woman.
The male-proposed stable matching is actually locally man-optimal and woman-pessimal, in the sense that any trade that a pair of women decide on would by definition make their current fiances worse off.
> How? They will be in the same school regardless of other students switching or not. And even if you didn’t strategize, you might receive an offer for an exchange, so you could even end up just as well as someone who did strategize.
In the sense that relative wellbeing matters to people in general. A system that provides half of people $1 and everyone else $10 makes people better in absolute terms, but worse off in relative terms, and that matters to people because access to many desirable goods in society depend on people's relative ranking.
This is a very well-understood effect and has been measured in different contexts, e.g. [3]
You are right that a person that does no strategizing may still receive an exchange offer, but it should be easy to show that in general, effective strategizing increases the probability of an exchange offer and the net quality of the school.
> I don’t get where this idea that globally the students will be better off if exchanging places is forbidden. Some people will be better off by exchanging, others will be in the same position as they were before. It’s clear that globally the system will have gained from more people being at their preferred schools.
I agree with you that exchanges increase welfare locally, and it would be nice to come up with a system that by definition come up with matches that are inherently stable to any pairwise trades, but as far as I'm aware there is no matching system that simultaneously does that and also effectively discourages strategic behavior (e.g. 'lying' about preferences). Game theory is full of proofs of the impossibility of simultaneously reaching 'obviously' desirable goals, e.g. [4].
Note that an equilibrium where consumers are honest about their preferences and then the 'matchmaker' can rely on those preferences is much simpler evaluate and optimize. This is why, for example, auctions are an effective way to find price—bids are generally close to 'honest' reflections of reservation prices.
As soon as broad strategic behavior comes into play, it's becomes much harder to determine whether your system is actually working well since the preferences no longer reflect what people really want.
A system where everyone is essentially masking their true preferences imposes obvious costs: everyone who doesn't strategize will be worse off relatively than those who do. Strategizing costs people time and energy. It also makes the matchmaker's job obviously harder, since the 'first step' would be to try to back out people's true preferences.
We can certainly argue about whether those costs are higher or lower than the cost of not sitting at a local optimum, but it seems unwise to simply deny that there is any tradeoff, or to completely ignore the fact that people care deeply about relative welfare as well as absolute welfare.
First, sorry for the "pout" in my previous response. It was supposed to be "point" but the spelling corrector disagreed.
I get the "relative well-being" argument, but honestly it doesn't change my mind. It seems to be an argument that puts jealousy in front of objective improvements. Extrapolating again, this is the dispute between those who think inequality is a problem in itself and those who think that as long as poverty is reduced, inequality doesn't matter.
I would be fine with a system that doesn't allow exchange as long as the situation described in the article wasn't allowed to happen (i.e. if there's a spot for me in my first preference, I won't be allocated to my second one).
I'll try to find time to read your references, thanks!
The situation here is not the same as what you describe, though, is it? Schools don't have preferences, they just have a number of available spots. I don't see how this cycle could happen in this case.
> If some bureaucrat thinks children should go to this or that school, we should do it because...?
Depends on the case. Sometimes parents are the best judges — but parents, like all of us, focus on local maximization, in this case, "what's best for my kids," and not what's best for all kids. Sometimes it's globally better for Alice not to be able to have the absolute best thing for her, because of the risk that this would produce worse outcomes for Bob, Carol, Dave, etc.
Dr. Atul Gawande wrote in one of his books that obstetricians decided that their job was not to achieve the absolute local-maximum best outcome for every individual mother — and therefore to use forceps for difficult deliveries, vice C-section surgery — but instead their mission was to seek a global maximum, i.e., the safe delivery of millions of babies per year. (Apparently it's difficult to be sure that trainee physicians have the proper "feel" for handling forceps, which if mishandled can result in catastrophic injuries to baby and mother.)
So, the OB community redefined the standard of care for difficult births as the C-section, which is much easier to teach and monitor. This means that some individual mothers will have surgery that they could have avoided through the use of forceps. But that's considered less important than avoiding the risk of the damage that improper use of forceps can cause.
> Would you prevent Alice and Bob from experiencing schools that are perfect matches for their abilities? Shouldn’t this be their or their parents’ call?
Again this focuses too narrowly on the local maximum. Sometimes parents are in the best position to make the call. But sometimes we as a society insist that parental judgments stay within certain guard rails; that's why, for example, we have compulsory-education laws. (And it goes without saying that we don't assume the kids are the best judges.)
It seems unlikely that this was the case in this instance. You could argue about future lotteries, but it would make more sense to have a system design to avoid these situations.
If you and I have each other’s first selection, then we should have been assigned them in the first place.
Not if their swap implicitly makes everyone else worse off though; and this is precisely the claim that judges make, that you cannot simply isolate the effects of the swap without considering the global consequences of the state of the 'game', so to speak.