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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]The same number of students get into the desirable spots either way in this scenario.  Thus, every student still has the same chance to get one of the 12 spots.  The only difference is that with one lottery you know earlier whether you got into your chosen school, a different school, or got shut out.  [/quote]

You still don't understand the difference between one single student's odds of getting into 12 schools in 12 different lotteries vs. 12 schools in 1 lottery.  No one is arguing the fact that at the end of the day, there are only X number of spots with Y numbers of people looking and only X students will end up in those spots.  Yes, we all understand that part.[/quote]

Each lottery is for only a fraction of the total pot.  Thus the chances in each individual lottery are less than the chances of getting into any of the schools in the larger lottery.

Ex.  2 schools, 1 space in each.  10 students applying.  If there are two lotteries, the student has a 1 in 10 chance of getting into school A and a 1 in 10 chance of getting into school B.  Thus, the student has a 2 in 10 (1 in 5) chance of getting into either school.  If there is one lottery, the student has a 2 in 10 (or 1 in 5) chance of getting into one of the schools.  See how it is the same.  Do you need another example?[/quote]

You're assuming that all things are equal in this example.  They are not.  Under the old system, child had a 1 in 10 chance at one school and a 1 in 500 chance at another school and each of those odds operated independently of each other.  Under the new system with the single draw, a poor number rules them out of every single option, even the ones where the odds would have been pretty good.[/quote]

But you are missing part of the equation. First, because you can only choose 12 schools, not every student will be in every pool. That reduces the size of some pools. And secondly, after each round, a certain number of students have been matched and are no longer in the pools, thereby increasing the odds of a match for students who are still in the mix.[/quote]

Different PP than the one you're responding to, but while the points you make are true, you are still missing the prior PP's point, which is also true.  Even though not every student will be in every pool, for whatever pool you ARE in, having a bad number shuts you out of everything, usually even you're #12 choice.  Whereas before, even if you still only applied to 12 schools, 12 different lotteries meant you had a brand new chance at a good number in each lottery.  That, in and of itself, improves the odds you'll do well.  Doesn't increase the spots, doesn't reduce the number of applicants overall.  But in each lottery it means you have a new chance to do well, as opposed to just one shot to do well that impacts all your choices.

Not saying one system is better than the other, just pointing out that it is INcorrect to say the odds are the same under both systems.  They are not the same.[/quote]

And how do you define "do well"? Because there aren't any additional seats in the individual lotteries. And each child can only occupy one chair. And there aren't enough spots at the coveted schools for everyone to feel like they're "doing well," no matter which kind of lottery you're running.

So you're defining "do well" as having a waitlist number that makes you feel better?[/quote]

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