The downside of the DC school lottery

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Still, the one-number-per-year thing is a real bummer of the current system.

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people.

In this hypothetical, you are correct. Only one flip is the best procedure.

But your hypothetical is flawed. The true situation is that there are many schools. So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die. Would you rather have one roll, and if it turned up badly you got shut out of all your choices? Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote: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.

Ding ding ding ding! This is the correct answer. All the rest of you are wrong. OP, you’d need to argue against this suboptimal outcome. You can’t. You lose.

All the rest of you are also wrong.

OP here. You’re right.

If the algorithm uses more than one lottery number, this situation can occur. This is a “non-stable assignment”.

Ok, makes sense. It’s still bad that kids get one lottery number for all schools per year. Seems pretty sub-optimal.

It occurs to me that the algorithm is a deferred-assignment algorithm. So I think the problem you’ve mentioned above can be resolved by an additional round of swapping assignments to eliminate instability (of course, as in the current lottery system, this would all happen before any results are released.) Swapping could also occur for waitlist rankings to ensure stability. But that seems like a pretty complicated set of scenarios to try to ensure are non-game able.

Still, the one-number-per-year thing is a real bummer of the current system.

OMG. It is not the number of numbers that is causing some people to have a bad outcome! There are not enough high-quality seats and that is the problem. No lottery system is going to create more seats. No matter how the lottery works, someone is going to have a bad outcome and feel that the system is a bummer. Catch on already.

I’m sorry you don’t understand how mathematics works.

The whole lottery system is premised on the assumption that there are limited resources (seats) that need to be assigned in the best way possible.
We are talking about the mathematics behind the assignment algorithm.
While you are banging on about the premises.

That’s your right, I suppose, but it’s neither here nor there to the point of the thread.
Please don’t help your child or other children do math word problems, as with logic like this you’ll just confuse them. I am sure you’re a very good attorney, however, and god knows we need some of those now.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Still, the one-number-per-year thing is a real bummer of the current system.

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people.

In this hypothetical, you are correct. Only one flip is the best procedure.

But your hypothetical is flawed. The true situation is that there are many schools. So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die. Would you rather have one roll, and if it turned up badly you got shut out of all your choices? Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

It wouldn't matter. The odds of getting into a desirable school would be the same either way. There are still the same number of seats and the same number of entries. You would not have a better chance of getting into one of the 12 schools on your list this way.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Still, the one-number-per-year thing is a real bummer of the current system.

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people.

In this hypothetical, you are correct. Only one flip is the best procedure.

But your hypothetical is flawed. The true situation is that there are many schools. So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die. Would you rather have one roll, and if it turned up badly you got shut out of all your choices? Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

It wouldn't matter. The odds of getting into a desirable school would be the same either way. There are still the same number of seats and the same number of entries. You would not have a better chance of getting into one of the 12 schools on your list this way.

^^ Failure to understand mathematics

I’m done here. Take a stats or applied math class please. Pay attention in sections on “correlated outcomes”

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Still, the one-number-per-year thing is a real bummer of the current system.

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people.

In this hypothetical, you are correct. Only one flip is the best procedure.

But your hypothetical is flawed. The true situation is that there are many schools. So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die. Would you rather have one roll, and if it turned up badly you got shut out of all your choices? Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

The downside in your scenario is "being shut out at all of them." So let me tweak your game a little: say you get to rank as many schools as you want, and then roll the 100-sided die once. Is that better or worse than picking the same number of schools, and rolling the 100-sided die for each of them? I say it's the same, it just doesn't take as long. (It can be shown using induction that if everyone picks the same number the odds are exactly the same in both scenarios). In each scenario you run the risk of being shut out, which decreases as the number of picks increases.

In the real world, n=12. Most people don't use all twelve picks. The reason people get shut out is not because twelve is too small, or because they don't get enough rolls of the dice, but because they get poor lottery numbers and there aren't enough good seats in the system.

What seems to underlie your argument is a belief that somehow the current system over-rewards people with good lottery numbers, that a fairer system would spread the wealth more equitably. You've repeatedly referred to people with good numbers getting into "all" of their choices. But people with good numbers get into exactly one school. There is no way to divide that one seat more finely and spread the wealth.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Still, the one-number-per-year thing is a real bummer of the current system.

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people.

In this hypothetical, you are correct. Only one flip is the best procedure.

But your hypothetical is flawed. The true situation is that there are many schools. So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die. Would you rather have one roll, and if it turned up badly you got shut out of all your choices? Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

It wouldn't matter. The odds of getting into a desirable school would be the same either way. There are still the same number of seats and the same number of entries. You would not have a better chance of getting into one of the 12 schools on your list this way.

^^ Failure to understand mathematics

I’m done here. Take a stats or applied math class please. Pay attention in sections on “correlated outcomes”

I have a degree in mathematics from Harvard and the PP is exactly right -- the odds are exactly the same. Show your work or don't call names.

Proof by induction:

Assume every participant in the lottery can pick one school. You are competing against only people who picked the same school as you. Regardless of whether it is one roll per school or one roll for the whole lottery, you have one roll and you get the spot if you roll the highest in your group. So the odds are exactly the same.

Assume that it is true that if everyone picks n schools the odds are the same for one roll or 100 rolls. Does that imply that they are the same for n+1? The outcome we are assessing is whether you get shut out, so we are looking at whether the odds of getting the seat at your n+1 choice change depending on whether there are 100 rolls or one roll. In either case the pool of competitors is the same, and the person with the highest roll in that group gets the seat. So again the odds are exactly the same.

Since the hypothesis is true when n=1, and it has been shown that the hypothesis being true for n implies it is true for n+1, the hypothesis is proved.

[Anonymous]

Ok but I do kinda get what the OP is saying even though earlier I argued that his idea is flawed.

Case in point, we had a terrible master number. But thankfully we got into LAMB separately. Many people kinda had two chances and were equally glad if they managed to get in.

I now however realize we are probably attending school with at least a few people who would’ve rather been someplace else since it wasn’t ranked by preference. I think the point is, you either have this all or nothing master number situation, with winners and losers, or you have a lot of people who are kind of ok with where they’re at but it wasn’t their first choice. I also have been that person who has a great master number and kind of does get in everywhere because waitlist offers keep arising. I don’t know if there’s any way to soften the blow of a bad number but having at least one other roll of the dice feels like it.

[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.

that won't happen until most of the the kids peers were acceptable to most parents.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Still, the one-number-per-year thing is a real bummer of the current system.

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people.

In this hypothetical, you are correct. Only one flip is the best procedure.

But your hypothetical is flawed. The true situation is that there are many schools. So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die. Would you rather have one roll, and if it turned up badly you got shut out of all your choices? Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

It wouldn't matter. The odds of getting into a desirable school would be the same either way. There are still the same number of seats and the same number of entries. You would not have a better chance of getting into one of the 12 schools on your list this way.

^^ Failure to understand mathematics

I’m done here. Take a stats or applied math class please. Pay attention in sections on “correlated outcomes”

I have a degree in mathematics from Harvard and the PP is exactly right -- the odds are exactly the same. Show your work or don't call names.

Proof by induction:

Assume every participant in the lottery can pick one school. You are competing against only people who picked the same school as you. Regardless of whether it is one roll per school or one roll for the whole lottery, you have one roll and you get the spot if you roll the highest in your group. So the odds are exactly the same.

Assume that it is true that if everyone picks n schools the odds are the same for one roll or 100 rolls. Does that imply that they are the same for n+1? The outcome we are assessing is whether you get shut out, so we are looking at whether the odds of getting the seat at your n+1 choice change depending on whether there are 100 rolls or one roll. In either case the pool of competitors is the same, and the person with the highest roll in that group gets the seat. So again the odds are exactly the same.

Since the hypothesis is true when n=1, and it has been shown that the hypothesis being true for n implies it is true for n+1, the hypothesis is proved.

Look you too are making a hash of this math and making Harvard look bad.

Your discrete-math arguments do not apply to reasoning about probabilities. Your induction argument fails because the n case is statistically dependent on the n+1 case, so you cannot assume the n case to be true when proving the n+1.

What you want to do instead is calculate the VARIANCE of outcomes with 1 roll or 100 rolls for 100 schools. You are correct that the number of seats does not change so the number of students given a seat does not change. What changes is the ordering and the waitlist positions. To see this, look at the kid with the lowest 1-roll master number. They are last on all their waitlists. That situation does not happen if there are multiple rolls.

Again, it’s been discussed above that the situation above is suboptimal from a lottery point of view (it is unstable). So don’t take it too seriously. But the posts above about fixed number of seats are just missing the point.

I guess the take home here from this thread is: yes, reasoning about probability and stochastic processes is hard.

[Anonymous]

But the posts above about fixed number of seats are just missing the point.

we can take the posts above about “make all the schools better!!!” and draw an analogy to the NBA lottery.


While some of us are discussing how the lottery might be tweaked to improve it, the “schools all better” crowd is basically saying
“MAKE ALL THE PLAYERS BETTER ... IF WE HAD 100 KOBE BRYANTS IN EVERY LOTTERY THERE WOULD BE NO NEED FOR A LOTTERY!!!!!”

Well, yes, that is true. Noted.

[Anonymous]

Anonymous wrote:Ok but I do kinda get what the OP is saying even though earlier I argued that his idea is flawed.

Case in point, we had a terrible master number. But thankfully we got into LAMB separately. Many people kinda had two chances and were equally glad if they managed to get in.

I now however realize we are probably attending school with at least a few people who would’ve rather been someplace else since it wasn’t ranked by preference. I think the point is, you either have this all or nothing master number situation, with winners and losers, or you have a lot of people who are kind of ok with where they’re at but it wasn’t their first choice. I also have been that person who has a great master number and kind of does get in everywhere because waitlist offers keep arising. I don’t know if there’s any way to soften the blow of a bad number but having at least one other roll of the dice feels like it.

But you might be happier with another school, say DC Bilingual. And someone at DC Bilingual might prefer LAMB. So LAMB opting out of the lottery made you both worse off.

It still goes back to the number of seats. There's no way to make everyone happy, but at least the common lottery makes more people happy. Or less miserable.

-NP

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Still, the one-number-per-year thing is a real bummer of the current system.

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people.

In this hypothetical, you are correct. Only one flip is the best procedure.

But your hypothetical is flawed. The true situation is that there are many schools. So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die. Would you rather have one roll, and if it turned up badly you got shut out of all your choices? Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

It wouldn't matter. The odds of getting into a desirable school would be the same either way. There are still the same number of seats and the same number of entries. You would not have a better chance of getting into one of the 12 schools on your list this way.

^^ Failure to understand mathematics

I’m done here. Take a stats or applied math class please. Pay attention in sections on “correlated outcomes”

I have a degree in mathematics from Harvard and the PP is exactly right -- the odds are exactly the same. Show your work or don't call names.

Proof by induction:

Assume every participant in the lottery can pick one school. You are competing against only people who picked the same school as you. Regardless of whether it is one roll per school or one roll for the whole lottery, you have one roll and you get the spot if you roll the highest in your group. So the odds are exactly the same.

Assume that it is true that if everyone picks n schools the odds are the same for one roll or 100 rolls. Does that imply that they are the same for n+1? The outcome we are assessing is whether you get shut out, so we are looking at whether the odds of getting the seat at your n+1 choice change depending on whether there are 100 rolls or one roll. In either case the pool of competitors is the same, and the person with the highest roll in that group gets the seat. So again the odds are exactly the same.

Since the hypothesis is true when n=1, and it has been shown that the hypothesis being true for n implies it is true for n+1, the hypothesis is proved.

Ummmm, we are supposed to be impressed? Could you not get into MIT?

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Still, the one-number-per-year thing is a real bummer of the current system.

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people.

In this hypothetical, you are correct. Only one flip is the best procedure.

But your hypothetical is flawed. The true situation is that there are many schools. So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die. Would you rather have one roll, and if it turned up badly you got shut out of all your choices? Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

It wouldn't matter. The odds of getting into a desirable school would be the same either way. There are still the same number of seats and the same number of entries. You would not have a better chance of getting into one of the 12 schools on your list this way.

^^ Failure to understand mathematics

I’m done here. Take a stats or applied math class please. Pay attention in sections on “correlated outcomes”

I have a degree in mathematics from Harvard and the PP is exactly right -- the odds are exactly the same. Show your work or don't call names.

Proof by induction:

Assume every participant in the lottery can pick one school. You are competing against only people who picked the same school as you. Regardless of whether it is one roll per school or one roll for the whole lottery, you have one roll and you get the spot if you roll the highest in your group. So the odds are exactly the same.

Assume that it is true that if everyone picks n schools the odds are the same for one roll or 100 rolls. Does that imply that they are the same for n+1? The outcome we are assessing is whether you get shut out, so we are looking at whether the odds of getting the seat at your n+1 choice change depending on whether there are 100 rolls or one roll. In either case the pool of competitors is the same, and the person with the highest roll in that group gets the seat. So again the odds are exactly the same.

Since the hypothesis is true when n=1, and it has been shown that the hypothesis being true for n implies it is true for n+1, the hypothesis is proved.

Ummmm, we are supposed to be impressed? Could you not get into MIT?

That's exactly what my mom said too.

[Anonymous]

Anonymous wrote:
I guess the take home here from this thread is: yes, reasoning about probability and stochastic processes is hard.

No, the takeaway is you are a stubborn person. You got an idea into your head. You find it impossible to believe your idea is wrong, so you go on all sorts of logical excursions -- and throw in insults to those who try to set you straight, to boot.

Your logical fallacy is in this paragraph, in the bolded part:

What you want to do instead is calculate the VARIANCE of outcomes with 1 roll or 100 rolls for 100 schools. You are correct that the number of seats does not change so the number of students given a seat does not change. What changes is the ordering and the waitlist positions. To see this, look at the kid with the lowest 1-roll master number. They are last on all their waitlists. That situation does not happen if there are multiple rolls.

Having more rolls doesn't affect the variance of outcomes. It affects the variance of the numbers used to determine the outcomes. With a single roll you get a linear distribution, with more rolls you get more of a normal distribution. But when you take those numbers are rank the participants, the outcome is the same: someone is first, someone is last, and only some of the participants get a seat because there are more participants than seats.

The ordering and waitlist positions aren't important, what's important is whether you get a seat or not. It does you no good to have a good waitlist position if the waitlist doesn't move. You seem to be obsessed with the idea that the lottery lets those with good number "hoard" good fortune, which could more equitably be distributed to the less fortunate. But that's not how it works. Everyone gets either one seat, or no seat. There is no way to distribute them more granularly.

I'm assuming you're obsessing over this because you got a bad lottery number and just can't accept that you're unlucky rather than the system being broken. I'm sorry you got a bad number, better luck next time. But this is a strange thing to obsess over. As another poster pointed out, the lottery is one of the best-functioning things in all of public education in DC. And it has consistently gotten better in recent years. If you want to get upset, there are lots of bigger issues to get upset about.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Still, the one-number-per-year thing is a real bummer of the current system.

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people.

In this hypothetical, you are correct. Only one flip is the best procedure.

But your hypothetical is flawed. The true situation is that there are many schools. So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die. Would you rather have one roll, and if it turned up badly you got shut out of all your choices? Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

It wouldn't matter. The odds of getting into a desirable school would be the same either way. There are still the same number of seats and the same number of entries. You would not have a better chance of getting into one of the 12 schools on your list this way.

^^ Failure to understand mathematics

I’m done here. Take a stats or applied math class please. Pay attention in sections on “correlated outcomes”

I have a degree in mathematics from Harvard and the PP is exactly right -- the odds are exactly the same. Show your work or don't call names.

Proof by induction:

Assume every participant in the lottery can pick one school. You are competing against only people who picked the same school as you. Regardless of whether it is one roll per school or one roll for the whole lottery, you have one roll and you get the spot if you roll the highest in your group. So the odds are exactly the same.

Assume that it is true that if everyone picks n schools the odds are the same for one roll or 100 rolls. Does that imply that they are the same for n+1? The outcome we are assessing is whether you get shut out, so we are looking at whether the odds of getting the seat at your n+1 choice change depending on whether there are 100 rolls or one roll. In either case the pool of competitors is the same, and the person with the highest roll in that group gets the seat. So again the odds are exactly the same.

Since the hypothesis is true when n=1, and it has been shown that the hypothesis being true for n implies it is true for n+1, the hypothesis is proved.

Look you too are making a hash of this math and making Harvard look bad.

Your discrete-math arguments do not apply to reasoning about probabilities. Your induction argument fails because the n case is statistically dependent on the n+1 case, so you cannot assume the n case to be true when proving the n+1.

What you want to do instead is calculate the VARIANCE of outcomes with 1 roll or 100 rolls for 100 schools. You are correct that the number of seats does not change so the number of students given a seat does not change. What changes is the ordering and the waitlist positions. To see this, look at the kid with the lowest 1-roll master number. They are last on all their waitlists. That situation does not happen if there are multiple rolls.

Again, it’s been discussed above that the situation above is suboptimal from a lottery point of view (it is unstable). So don’t take it too seriously. But the posts above about fixed number of seats are just missing the point.

I guess the take home here from this thread is: yes, reasoning about probability and stochastic processes is hard.

OMG. I am not even the PP and you are driving me insane. You are wrong. You can only get into one school in the end. Getting a number so bad you are shut out of every school you apply to is statistically the same thing/just as likely as getting the number of independent rolls required to shut you out of every school. That's the whole point. Many people don't end up at their #1 school or shut out entirely, they get into a school somewhere in the middle of their list... akin to getting the combo of independent rolls that gets them into some schools and not others w/ a rule that you can only take the seat at the school you preferred most. THAT'S THE WHOLE POINT OF THE LOTTERY. Yes, there is only one master number, but it essentially enters you into independent lotteries for each school. Whether you get different master numbers for each independent lottery or one master number does not affect your odds of getting into a school.