The downside of the DC school lottery

[Anonymous]

There’s several reasons.

Though the biggest problem with the way the DC lottery is set up is this:
Every child only gets one shot per year— one number per year.
So if the number is low, the kid gets none of their choices. And if the number is high, the kid could effectively choose any of their choices.

This is an issue with the algorithm.

One could certainly imagine a lottery system where kids get one number for each SCHOOL they choose, mitigating risk and allowing a new shot at every school — not just a totally correlated slate of outcomes, all good or all bad.

I’ve heard the “designed by Harvard/MIT/Caltech profs” story. Yes, that’s all fine. But there’s still room for improving the algorithm.

So here’s a proposed algorithm tweak: for every school a child ranks in the lottery, generate a number (eg a number between zero and 1). That number is the lottery number that this child uses for this school. Then do the assignments exactly as they’re done in the current system. Whenever an assignment is computed for a child at at school, use this child-school assigned number. When assignment for a child is computed at a different school, use the child-school assigned number for that pair. The ranking system to decide assignments would still be the same, just using a “child-school” number rather than a “child” number.

Pros: kids no longer have “bad” lottery years and “good” lottery years. They get multiple bites of the apple in each year.
Cons: kids that list 10 schools have a better chance of matching somewhere they want than kids who list one school. But isn’t that what we want anyway?

I don’t see any other clear ways to manipulate this proposed lottery algorithm. Are there any? I suppose the system is a little less transparent than the current system— it’s almost impossible to use public data to figure out how it would be working, because you can no longer estimate any single master lottery number from published data.

[Anonymous]

The biggest issue is there just aren't enough good enough schools. The lottery would be a non-issue if most of the seats in the system were acceptable to most parents.

[Anonymous]

Anonymous wrote:The biggest issue is there just aren't enough good enough schools. The lottery would be a non-issue if most of the seats in the system were acceptable to most parents.

Ok but that’s not a lottery issue. That in some ways is the discussion topic for this whole board, not just this thread.

Question is whether the lottery algorithm is optimal.

[Anonymous]

Anonymous wrote:
So if the number is low, the kid gets none of their choices. And if the number is high, the kid could effectively choose any of their choices.

That's not how the current algorithm works. If the number is high the kid gets assigned to the school that the kid ranked the highest that has a spot. There is no choice.

[Anonymous]

Anonymous wrote:

One could certainly imagine a lottery system where kids get one number for each SCHOOL they choose, mitigating risk and allowing a new shot at every school — not just a totally correlated slate of outcomes, all good or all bad.

A sucky lottery number is a sucky lottery number.

What you're proposing is more draws, but at the end of the day those with good draws get good outcomes and those with bad draws get bad outcomes. More draws doesn't increase the number of desirable seats.

[Anonymous]

Anonymous wrote:

Anonymous wrote:
So if the number is low, the kid gets none of their choices. And if the number is high, the kid could effectively choose any of their choices.

That's not how the current algorithm works. If the number is high the kid gets assigned to the school that the kid ranked the highest that has a spot. There is no choice.

Correct. The choice is effectively done on the front end— when the rankings are submitted.

The point is, if a kid has a good enough number to get into their first choice school, in many cases they would have also gotten into many or most of their lower choice schools. In other words: kids have good years or bad years in the lottery, because they get only one roll of the dice — one master number — per year.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

One could certainly imagine a lottery system where kids get one number for each SCHOOL they choose, mitigating risk and allowing a new shot at every school — not just a totally correlated slate of outcomes, all good or all bad.

A sucky lottery number is a sucky lottery number.

What you're proposing is more draws, but at the end of the day those with good draws get good outcomes and those with bad draws get bad outcomes. More draws doesn't increase the number of desirable seats.

Right. But more draws per year WOULD help a lot of students.

Say you have kids whose parents feel equally good about Mundo Verde and Yu Ying. In the current system, kids often do well enough to get into both, or poorly so they get into neither. (Due to different waitlists and desireability there is some gray area inbetween even with the current system.)

But if the kid got a number for each SCHOOL, then they’d have a separate roll of the dice for each. They could bomb in the Mundo lottery and do well in the YY lottery. And they’re more likely to end up in one school they want.

Any situation where a kid/parent has a few choices that are relatively equally competitive, and relatively similarly ranked by the kid/parent, would be improved by the child-school lottery number system.

[Anonymous]

Your system is what there used to be. It was less good because there were kids who could be swapped with each other and both of them would be better off; that can no longer happen.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

One could certainly imagine a lottery system where kids get one number for each SCHOOL they choose, mitigating risk and allowing a new shot at every school — not just a totally correlated slate of outcomes, all good or all bad.

A sucky lottery number is a sucky lottery number.

What you're proposing is more draws, but at the end of the day those with good draws get good outcomes and those with bad draws get bad outcomes. More draws doesn't increase the number of desirable seats.

Right. But more draws per year WOULD help a lot of students.

Say you have kids whose parents feel equally good about Mundo Verde and Yu Ying. In the current system, kids often do well enough to get into both, or poorly so they get into neither. (Due to different waitlists and desireability there is some gray area inbetween even with the current system.)

But if the kid got a number for each SCHOOL, then they’d have a separate roll of the dice for each. They could bomb in the Mundo lottery and do well in the YY lottery. And they’re more likely to end up in one school they want.

Any situation where a kid/parent has a few choices that are relatively equally competitive, and relatively similarly ranked by the kid/parent, would be improved by the child-school lottery number system.

Nobody gets into both.

[Anonymous]

I think where your confused is you think that someone with a high lottery number gets into all of their choices, and that someone else is kept from getting those seats. That's not how it works. Someone with a high lottery number gets into their first choice.

Changing the way the draw is done doesn't change the number of seats. The only question to ask about a system is whether once it's all done, are there any two people who would be willing to trade with each other and each be happier? If so, then the system is flawed.

The current system is designed so that it never happens that mutually beneficial trades exist, so long as people put in their true preferences. That also means that strategizing or gaming is impossible, the best outcome for any individual is to put in their true preference.

[Anonymous]

Anonymous wrote:I think where your confused is you think that someone with a high lottery number gets into all of their choices, and that someone else is kept from getting those seats. That's not how it works. Someone with a high lottery number gets into their first choice.

Changing the way the draw is done doesn't change the number of seats. The only question to ask about a system is whether once it's all done, are there any two people who would be willing to trade with each other and each be happier? If so, then the system is flawed.

The current system is designed so that it never happens that mutually beneficial trades exist, so long as people put in their true preferences. That also means that strategizing or gaming is impossible, the best outcome for any individual is to put in their true preference.

This. Every year there is at least one poster on DCUM who posts something like this. Because your very basic understanding is clearly superior to the Nobel prize winning algorithm designed to prevent gaming and reward only true preference.

Every kid can only occupy one seat. Period.

It isn't your ignorance that bothers me, it is how confident you are in it.

[Anonymous]

Anonymous wrote:I think where your confused is you think that someone with a high lottery number gets into all of their choices, and that someone else is kept from getting those seats. That's not how it works. Someone with a high lottery number gets into their first choice.

Changing the way the draw is done doesn't change the number of seats. The only question to ask about a system is whether once it's all done, are there any two people who would be willing to trade with each other and each be happier? If so, then the system is flawed.

The current system is designed so that it never happens that mutually beneficial trades exist, so long as people put in their true preferences. That also means that strategizing or gaming is impossible, the best outcome for any individual is to put in their true preference.

Seems pretty clear to me the discussion is about increasing draws while maintaining the true preference system.

The current system has one draw per year per child.
The proposed system has one draw per school per year per child.

It’s not about “getting into all of their choices”.
It’s about hedging risk and preventing total “bad years” for students in the lottery.

It appears the best outcome for any individual in the proposed system is also to put in their true preference.

So far, we haven’t seen any legitimate criticisms of the proposal, just some critiques based on poor understanding. (I think it’s likely there are some downsides with the proposal — just none have yet been brought forth.)

[Anonymous]

Anonymous wrote:

Anonymous wrote:I think where your confused is you think that someone with a high lottery number gets into all of their choices, and that someone else is kept from getting those seats. That's not how it works. Someone with a high lottery number gets into their first choice.

Changing the way the draw is done doesn't change the number of seats. The only question to ask about a system is whether once it's all done, are there any two people who would be willing to trade with each other and each be happier? If so, then the system is flawed.

The current system is designed so that it never happens that mutually beneficial trades exist, so long as people put in their true preferences. That also means that strategizing or gaming is impossible, the best outcome for any individual is to put in their true preference.

This. Every year there is at least one poster on DCUM who posts something like this. Because your very basic understanding is clearly superior to the Nobel prize winning algorithm designed to prevent gaming and reward only true preference.

Every kid can only occupy one seat. Period.

It isn't your ignorance that bothers me, it is how confident you are in it.

Yes- this gets posted every year!

[Anonymous]

The system the OP is describing is (I think) pretty close to what DC used to do when each school ran its own lottery. it was a mess. The biggest issue from an economics point of view is that it led to a situation where there could have been a lot of mutually beneficial trades -- which means it was inefficient at allocating a scarce resource. For example under the old system it was entirely possible for the following scenario to take place:

KidA gets into MV and has a bad waitlist number for IT, his parents prefer IT

KidB gets into IT and has a bad waitlist number for MV, his parents prefer MV

Under the new system, that won't happen because the parents will rank their choices and if KidA has a good number, he will rank IT first and get in there. KidB would get into MV with a good number.

[Anonymous]

Anonymous wrote:

Anonymous wrote:I think where your confused is you think that someone with a high lottery number gets into all of their choices, and that someone else is kept from getting those seats. That's not how it works. Someone with a high lottery number gets into their first choice.

Changing the way the draw is done doesn't change the number of seats. The only question to ask about a system is whether once it's all done, are there any two people who would be willing to trade with each other and each be happier? If so, then the system is flawed.

The current system is designed so that it never happens that mutually beneficial trades exist, so long as people put in their true preferences. That also means that strategizing or gaming is impossible, the best outcome for any individual is to put in their true preference.

Seems pretty clear to me the discussion is about increasing draws while maintaining the true preference system.

The current system has one draw per year per child.
The proposed system has one draw per school per year per child.

It’s not about “getting into all of their choices”.
It’s about hedging risk and preventing total “bad years” for students in the lottery.

It appears the best outcome for any individual in the proposed system is also to put in their true preference.

So far, we haven’t seen any legitimate criticisms of the proposal, just some critiques based on poor understanding. (I think it’s likely there are some downsides with the proposal — just none have yet been brought forth.)

Yes, PPs above have pointed out some logical problems with the proposed system: it will lead to situations where there are mutually beneficial trades. For example, imagine there are two students who each rank two schools:

Student 1: School A, School B
Student 2: School B, School A

Now imagine there is only one seat left at both schools. Under the proposed system, it is possible that Student 1 could end up at B and Student 2 could end up at A, meaning both students got their less desirable choice. This would happen if each student got a poor draw for their respective first choice school and a great draw for their second choice school.

Under the current system, this outcome is not possible. With the hypothetical rankings above, Student 1 will always be matched to A and Student 2 always to B, which is everyone's preferred outcome.

One more point about "good" lottery years and "bad" lottery years. A good lottery year is when you get into a desired school and a bad lottery year is when you do not. By changing the lottery algorithm, you are not increasing the number of school seats a given person finds desirable, nor are you decreasing the number of kids vying for those seats. Therefore, my odds of having a good year (getting into a school I like) are not improved one bit. Hedging risks is something you can do with investments or crops, because you can diversify and spread them around. You can't do that here, because you are trying to place exactly one child into one seat.