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> This is culturally alien to me; the students receiving the benefit are not harming other students. It's not just "culturally alien"; it's a straight-up error

> This is culturally alien to me; the students receiving the benefit are not harming other students. It's not just "culturally alien"; it's a straight-up error. > Solution: only allow trades that are in accord with the students' submitted preferences. That is, if Alice prefers Central to Devonshire, and Bob prefers Devonshire to Central, then we could allow Alice and Bob to switch if their submitted rankings indicated that these moves were consistent with their desires. There would be no incentive to lie. It's not obvious to me that this is true? Relevant discussion over on /r/math: https://www.reddit.com/r/math/comments/6uyfle/why_a_dutch_court_stopped_high_school_students/dlwtroo/ https://www.reddit.com/r/math/comments/6uyfle/why_a_dutch_co...

s17n 9y ago
>> Solution: only allow trades that are in accord with the students' submitted preferences. That is, if Alice prefers Central to Devonshire, and Bob prefers Devonshire to Central, then we could allow Alice and Bob to switch if their submitted rankings indicated that these moves were consistent with their desires. There would be no incentive to lie. >It's not obvious to me that this is true? Even if you could solve the game theory issues, you wouldn't solve the problem of people selling spots in desirable schools.
cortesoft 9y ago
Wait, why is that a 'straight-up error'? They explained why it would harm other students - because it would incentivize students to choose popular schools instead of schools they actually wanted, in hopes of gaining a good trade opportunity. They don't want strategy to come into play, because some people are better at strategy than others. It isn't an 'error', it is just a decision that they don't want strategy to be a factor.
- Sniffnoy 9y ago
  Yes, the incentives this sets up could be bad for subsequent rounds; that is absolutely a real problem. But this passage seemed to be suggesting that trading, in and of itself, harmed students who were not involved in the trade, and that's not correct.
  - cortesoft 9y ago
    Something being unfair is not the same as something harming someone else. Lets say I have a cookie, and there are 10 kids in front of me who like cookies. If I give any kid a cookie for any reason, it doesn't HARM the kids who don't get a cookie; they are no better or worse off than if the cookie never existed. However, suppose I decide to give the cookie to the tallest kid - even though none of the other kids are harmed, this is still not a 'fair' situation. You can do no harm and still be unfair. Whether that is bad or not is subjective, but it is still unfair (in the sense that every kid has an equal chance at the cookie).
    - Sniffnoy 9y ago
      Sorry, I just realized that I failed to point out which part I was saying was "a straight-up error"; it's kind of buried in the sentence. My mistake! With emphasis this time: >By trading places, students could get another shot at a place. At schools for which they already had a go in the lottery. This would give them better chances. At the expense of students that don’t (or can’t) trade. This is unfair. The emphasized part is what I'm objecting to. Sorry about that.
      - cortesoft 9y ago
        Ok, I think we are having the exact same discussion in two threads. I will stop responding to this thread since I answered your objection in the other one :D
      - Retric 9y ago
        Let's say there is a lotto for concert tickets. If I pay 1,000 people to take part in that lotto who don't want the tickets then I get an 'unfair' advantage. The logic is similar for the school lotto as people would target schools based on their ability to trade not necessarily their actual preference. This would lower the odds of people who otherwise had fewer options. AKA, if only bob or sam want a spot sam's odds are 50/50%. But, of ted joins but would always give his spot to bob then sam's odds are 1/3 and bob's odds are 2/3.
    - 9y ago
LolWolf 9y ago
This would be a stable matching (after allowing these changes). Since Nash is guaranteed here, there would be no reason to lie on the original form, unless there's some weird mixed equilibrium (that's not pure). It'd be interesting to see what conditions we must have on it (if it even exists! I'm not sure to be honest), but the only pure equilibrium is certainly a stable matching.
lsiebert 9y ago
I'm curious if you could make trades automatic if all students involved benefited as per their preferences in such a way that it would be impossible to game. I think though that it would still be possible to game for any variant I can think up.
deleted 9y ago
[deleted]
norswap 9y ago
There's a word for that kind of error: the situation is not pareto-optimal. https://en.wikipedia.org/wiki/Pareto_efficiency https://en.wikipedia.org/wiki/Pareto_efficiency
- ucaetano 9y ago
  > the situation is not pareto-optimal. Only in the short run it isn't. On the long run, school trading creates incentives which make the entire system worse. So you're not just optimizing for a single round of students, you're optimizing for the future rounds of students. And pareto-optimal makes no sense when you're looking at future rounds with different students. But you could create a pareto-optimal analogy: allowing two students now to trade place in a seemingly pareto-optimal way would actually harm other students when you look at the future rounds, so the trade actually isn't pareto-optimal. So it isn't an error, it's working as intended.
  - om2 9y ago
    I think he's saying that the error is in the original assignment algorithm: it produces a solution that is not Parto-optimal. If it was, there would be no mutually advantageous trades. One way it could achieve that is by randomly doing mutually improving trades until none are left.
    - ucaetano 9y ago
      But you can't consider just the current round of students when designing such a system, you need to consider all subsequent rounds. In that case, allowing trades now leads to dissatisfaction in the future. So, while allowing trades now might seem to lead to a pareto-optimal scenario, it doesn't lead to a time-series-pareto-optimal scenario.
      - om2 9y ago
        The alternate system I described doesn't involve "allowing trades" and therefore can't create perverse incentives or affect subsequent rounds. The idea is to make an algorithm that performs a Pareto-optimal assignment algorithmically, so that no possible mutually advantageous trades exist when it is done. It's totally possible for an algorithm to do that, and the current Dutch one clearly doesn't. One possible way is to run the current algorithm, and then as long as the solution is not Pareto-optimal, perform a swap at random from the set of all pairs of students where swapping would improve both of their preferences. This can be proven to converge with sufficient steps. Doing this kind of swap algorithmically has nothing to do with "allowing trades". I'm calling them "swaps" instead of "trades" here to make clear there is no manual action involved on the part of the students. I hope this clarifies what I meant, and why objecting to "allowing trades" does not make sense as a response.
y7 9y ago
Suppose two students have identical rankings and end up with the same school. If one of them manages to trade (e.g. because they quickly manage to find someone that wants to trade with them), they have an advantage over the other student who is stuck with their lottery result. This is the unfairness the article talks about (besides the strategizing argument). Perhaps this can be remedied by automatic trading and another lottery, determining the order in which people get to trade, but that still doesn't solve the problem with strategic choices.
jpfed 9y ago
I no longer think it's true. https://news.ycombinator.com/item?id=15069370 https://news.ycombinator.com/item?id=15069370
mcherm 9y ago
> > This is culturally alien to me; the students receiving the benefit are not harming other students. > It's not just "culturally alien"; it's a straight-up error. Perhaps an exaggerated example will illustrate. Students are assigned by a lottery system that sometimes allows pairs (or triplets, etc) of students to have a beneficial trade. Then students are permitted to use dutch-school-trading.com to swap schools. Except that students who own computers are permitted to engage in this extra round of trading while students who do not own computers are not. Some consider this to be biased against students who don't own a computer. In reality, it's not the single factor of "owns a computer" which is at play, but multiple issues including social connectedness, strategic thinking, free time on the day the placements are published, and so forth.

s17n 9y ago

>> Solution: only allow trades that are in accord with the students' submitted preferences. That is, if Alice prefers Central to Devonshire, and Bob prefers Devonshire to Central, then we could allow Alice and Bob to switch if their submitted rankings indicated that these moves were consistent with their desires. There would be no incentive to lie. >It's not obvious to me that this is true? Even if you could solve the game theory issues, you wouldn't solve the problem of people selling spots in desirable schools.

cortesoft 9y ago

Wait, why is that a 'straight-up error'? They explained why it would harm other students - because it would incentivize students to choose popular schools instead of schools they actually wanted, in hopes of gaining a good trade opportunity. They don't want strategy to come into play, because some people are better at strategy than others. It isn't an 'error', it is just a decision that they don't want strategy to be a factor.

Sniffnoy 9y ago
Yes, the incentives this sets up could be bad for subsequent rounds; that is absolutely a real problem. But this passage seemed to be suggesting that trading, in and of itself, harmed students who were not involved in the trade, and that's not correct.
- cortesoft 9y ago
  Something being unfair is not the same as something harming someone else. Lets say I have a cookie, and there are 10 kids in front of me who like cookies. If I give any kid a cookie for any reason, it doesn't HARM the kids who don't get a cookie; they are no better or worse off than if the cookie never existed. However, suppose I decide to give the cookie to the tallest kid - even though none of the other kids are harmed, this is still not a 'fair' situation. You can do no harm and still be unfair. Whether that is bad or not is subjective, but it is still unfair (in the sense that every kid has an equal chance at the cookie).
  - Sniffnoy 9y ago
    Sorry, I just realized that I failed to point out which part I was saying was "a straight-up error"; it's kind of buried in the sentence. My mistake! With emphasis this time: >By trading places, students could get another shot at a place. At schools for which they already had a go in the lottery. This would give them better chances. At the expense of students that don’t (or can’t) trade. This is unfair. The emphasized part is what I'm objecting to. Sorry about that.
    - cortesoft 9y ago
      Ok, I think we are having the exact same discussion in two threads. I will stop responding to this thread since I answered your objection in the other one :D
    - Retric 9y ago
      Let's say there is a lotto for concert tickets. If I pay 1,000 people to take part in that lotto who don't want the tickets then I get an 'unfair' advantage. The logic is similar for the school lotto as people would target schools based on their ability to trade not necessarily their actual preference. This would lower the odds of people who otherwise had fewer options. AKA, if only bob or sam want a spot sam's odds are 50/50%. But, of ted joins but would always give his spot to bob then sam's odds are 1/3 and bob's odds are 2/3.
  - 9y ago

LolWolf 9y ago

This would be a stable matching (after allowing these changes). Since Nash is guaranteed here, there would be no reason to lie on the original form, unless there's some weird mixed equilibrium (that's not pure). It'd be interesting to see what conditions we must have on it (if it even exists! I'm not sure to be honest), but the only pure equilibrium is certainly a stable matching.

lsiebert 9y ago

I'm curious if you could make trades automatic if all students involved benefited as per their preferences in such a way that it would be impossible to game. I think though that it would still be possible to game for any variant I can think up.

deleted 9y ago

[deleted]

norswap 9y ago

There's a word for that kind of error: the situation is not pareto-optimal. https://en.wikipedia.org/wiki/Pareto_efficiency https://en.wikipedia.org/wiki/Pareto_efficiency

ucaetano 9y ago
> the situation is not pareto-optimal. Only in the short run it isn't. On the long run, school trading creates incentives which make the entire system worse. So you're not just optimizing for a single round of students, you're optimizing for the future rounds of students. And pareto-optimal makes no sense when you're looking at future rounds with different students. But you could create a pareto-optimal analogy: allowing two students now to trade place in a seemingly pareto-optimal way would actually harm other students when you look at the future rounds, so the trade actually isn't pareto-optimal. So it isn't an error, it's working as intended.
- om2 9y ago
  I think he's saying that the error is in the original assignment algorithm: it produces a solution that is not Parto-optimal. If it was, there would be no mutually advantageous trades. One way it could achieve that is by randomly doing mutually improving trades until none are left.
  - ucaetano 9y ago
    But you can't consider just the current round of students when designing such a system, you need to consider all subsequent rounds. In that case, allowing trades now leads to dissatisfaction in the future. So, while allowing trades now might seem to lead to a pareto-optimal scenario, it doesn't lead to a time-series-pareto-optimal scenario.
    - om2 9y ago
      The alternate system I described doesn't involve "allowing trades" and therefore can't create perverse incentives or affect subsequent rounds. The idea is to make an algorithm that performs a Pareto-optimal assignment algorithmically, so that no possible mutually advantageous trades exist when it is done. It's totally possible for an algorithm to do that, and the current Dutch one clearly doesn't. One possible way is to run the current algorithm, and then as long as the solution is not Pareto-optimal, perform a swap at random from the set of all pairs of students where swapping would improve both of their preferences. This can be proven to converge with sufficient steps. Doing this kind of swap algorithmically has nothing to do with "allowing trades". I'm calling them "swaps" instead of "trades" here to make clear there is no manual action involved on the part of the students. I hope this clarifies what I meant, and why objecting to "allowing trades" does not make sense as a response.

y7 9y ago

Suppose two students have identical rankings and end up with the same school. If one of them manages to trade (e.g. because they quickly manage to find someone that wants to trade with them), they have an advantage over the other student who is stuck with their lottery result. This is the unfairness the article talks about (besides the strategizing argument). Perhaps this can be remedied by automatic trading and another lottery, determining the order in which people get to trade, but that still doesn't solve the problem with strategic choices.

jpfed 9y ago

I no longer think it's true. https://news.ycombinator.com/item?id=15069370 https://news.ycombinator.com/item?id=15069370

mcherm 9y ago

> > This is culturally alien to me; the students receiving the benefit are not harming other students. > It's not just "culturally alien"; it's a straight-up error. Perhaps an exaggerated example will illustrate. Students are assigned by a lottery system that sometimes allows pairs (or triplets, etc) of students to have a beneficial trade. Then students are permitted to use dutch-school-trading.com to swap schools. Except that students who own computers are permitted to engage in this extra round of trading while students who do not own computers are not. Some consider this to be biased against students who don't own a computer. In reality, it's not the single factor of "owns a computer" which is at play, but multiple issues including social connectedness, strategic thinking, free time on the day the placements are published, and so forth.