Common Lottery Algorithm

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The school rankings made by other parents/student have absolutely no affect on your capability of accepting a seat in the lottery. The only thing has an affect on your acceptance is as follows:

1) Someone with a better preference requests the same seat
2) You get accepted at a higher ranked school.

That's it. It doesn't matter what the rank of the school was in scenario #1. The algorithm ignores it. It's entirely possible that the kid accepted in scenario #1 moves on to another school (that he ranked higher) and you can get the seat back! That's how the algorithm works!

Source? What is your source that in this specific situation it works this way?

This was all linked to earlier in the thread

Post article about MySchoolDC
http://www.washingtonpost.com/local/education/dc-rolls-out-unified-enrollment-lottery-for-traditional-charter-schools/2013/11/19/448ee1e0-4ca7-11e3-9890-a1e0997fb0c0_story.html

Which talks about Al Roth, nobel prize wining economist and chairman of IIPSC, the company running the lottery
http://iipsc.org/

The publication page leads to an article about the New Orleans Lottery
http://www.nola.com/education/index.ssf/2012/04/centralized_enrollment_in_reco.html

Which contains this image giving the steps on how the algorithm run
http://media.nola.com/education_impact/photo/diagram-enrollment-041512jpg-aea0b995c0aa929b.jpg

Pay special attention to step 3, because that's the crux of it. You are ranked by your preference pool and your random lottery number. Your school ranking only comes into play after step 3. The whole thing loops until it can't do any more matching.

If you really want to read up on it, here is an academic paper also published on the IIPSC website:
https://www2.bc.edu/~sonmezt/sc_aerfinal.pdf

I've reviewed most of those, including step 3. It amazes me that so many of you completely don't get that the specific example we're talking about is not outlined in Step 3. The example, for the zillionth time, is:

Student A has sibling preferenc at school A but ranked it #3. Student A's randomly assigned lottery number is 10. Student A has no other preferences (adding part about lottery number and no other preferences just to further clarify the question). By the time Student A is being considered for school A, they have already not gotten spots at their 1st and 2nd choice schools.

Student B also has sibling preference at school A but ranked it #1. Student B's randomly assigned lottery number is 20. Student B has no other preferences.

Show me the official source that says either: "Student A will get the spot because their random lottery number is higher" or "Student B ranking school A will NOT give student B an advantage over Student A".

Don't just link, show the specific place where it is clearly stated/explained that Student A trumps B no matter what in this scenario.

[Anonymous]

Lottery number trumps unless a preference trumps, why is this so complicated?

[Anonymous]

Anonymous wrote:Lottery number trumps unless a preference trumps, why is this so complicated?

It's not.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:
Child #1 has sibling preference but ranked school ABC at #3, and didn't get into their #1-2.
Child #2 has no preferences but ranked school ABC at #1.

Who gets the seat at school ABC?

What if child #2's lottery number is higher than child #1's?

Child #1. Sibling preference trumps no preference every time.

I second this. 100% according to the logic of stable match. School ABC prefers Child #2 over #1 so this creates an equitable match for all parties involved.

We were arguing this point yesterday, but as of yesterday, who is disputing this part of it?

The part we are now disputing is this:
Same scenario as above EXCEPT Child #2 DOES have sibling preference. Who gets the spot then if both children have sibling preference but Child #1 ranked the school #3 and didn't get into 1-2, vs. Child #2 who ranked the school #1?

If you believe parent ranking has no effect beyond what order the computer tries to place you, you believe basically that at this point it's random. Those of us saying parent ranking matters are saying that in THIS scenario, Child #2 will get the spot. Hands down. And random computer assigned lottery number does not impact anything at this point.

If the students are equal in terms of preferences, the one with the better number will get the spot, no matter what ranking the parent put.

Notable that of all the people saying this, none of you have provided a source yet for why this specific point is true for this DC Common Lottery. Interesting, and frankly, makes every opinion that says parent ranking doesn't affect this scenario totally suspicious.

LOL. What are you trying to say? That someone here is trying to throw everyone off so they can get a better chance in the lottery?

Either way, you should rank your schools in order of your actual preferences.

The end.

[Anonymous]

doctors go through a matching algorithm nationwide, this kind of thing can function

[Anonymous]

It's quite complicated and quite simple:

This is how Gale/Shapley works from a logical approach wrote:
1) Assign lottery numbers to all students

2) Place students into preference pools

3) Sort students in each pool by lottery number

4) in the first pool, iterate the students in the first preference pool

5) if the school has seat for the student then remove a seat from the school/grade

6) move onto the second pool, etc and so on

7) whenever a student gets an acceptance into a higher ranked seat (1 over 2, 3 over 5, etc), the previous seat (from a lower rank) is added back into the pool of seats for that school/grade (this is where the student/parent school rankings come into play)

This loops and loops on 4-7 until no more students are asking a school for a seat or until no more students are being accepted. If there are 20,000 students then it can loop up to 20,000 times although I imagine that is a rare occurrence.

Since it's a deferred acceptance model a single student can ask for the same seat multiple times. They might not get the seat in the 1st, 2nd or 15,000th iteration but they could on the 15,001st. And that can have an effect an another student and so on an etc. It's also then entirely possible that on the 18,243rd time they give up that seat to take a better one and the whole thing loops again until the closing arguments are met. I believe what the algorithm does is simply this process by applying a mathematical methodology.

[Anonymous]

It is the same basic algorithm as the resident matching program. But this does not change that you should still order your preferences the same way you would if it were last year's system.

[Anonymous]

Anonymous wrote:
We were arguing this point yesterday, but as of yesterday, who is disputing this part of it?

The part we are now disputing is this:
Same scenario as above EXCEPT Child #2 DOES have sibling preference. Who gets the spot then if both children have sibling preference but Child #1 ranked the school #3 and didn't get into 1-2, vs. Child #2 who ranked the school #1?

If you believe parent ranking has no effect beyond what order the computer tries to place you, you believe basically that at this point it's random. Those of us saying parent ranking matters are saying that in THIS scenario, Child #2 will get the spot. Hands down. And random computer assigned lottery number does not impact anything at this point.

From the FAQ:

FAQ wrote:
How does the My School DC common lottery work?
Student-school matches are based on the number of spaces at each school; sibling, proximity, and other preferences; and each student’s choices. (Through the My School DC common lottery, the six DCPS specialized high schools admit students based on specific criteria.)

When there are more students than spaces at a school, students who have a preference (such as a sibling preference) will be the first to be offered spaces. Then, random selection decides which other students will be offered spaces.

Students will be matched with no more than one school. My School DC will try to match each student with their 1st choice, then their 2nd choice, and so on through the student’s list.


What are preferences (sibling preference, proximity preference, in-boundary preference)?
Students may have a preference at one or more schools. Students with a preference at a particular school are offered space at that school before students who don’t have a preference. There are four types of preferences:

Sibling preference (DCPS and public charter schools). Your child will have a sibling preference at a school where a sibling is currently enrolled. Some schools also offer a preference in the lottery and/or on the waiting list to siblings of accepted students. For example, if you have two children applying to the same school this year and one is accepted, the school may offer a preference to the accepted child’s brother or sister. These preferences vary by school, so if you have questions, it’s best to contact the school. If your child is admitted with a sibling preference, be prepared to prove that your children are siblings when you enroll them. (DCPS specialized high schools do not offer a sibling preference.)

Proximity preference (DCPS only). Your child will receive a preference if he or she lives within a reasonable walking distance of a school. (DCPS high schools do not offer a proximity preference.)

In-boundary preference (DCPS PK3 and PK4 only). PK3 and PK4 students receive a preference at their in-boundary DCPS schools.

Adams-boundary preference (Oyster-Adams Bilingual School only). In 2007, John Quincy Adams Elementary School merged with Oyster Bilingual School. Students living in the boundary of the former Adams Elementary School get a preference when applying to Oyster-Adams.

1. If two students have the same preference, lottery number determines which one gets it.
2. Ranking a school higher is not a preference.
3. In this scenario, the child with with the better lottery number gets the slot.

[Anonymous]

Anonymous wrote:
I've reviewed most of those, including step 3. It amazes me that so many of you completely don't get that the specific example we're talking about is not outlined in Step 3. The example, for the zillionth time, is:

Student A has sibling preference at school A but ranked it #3. Student A's randomly assigned lottery number is 10. Student A has no other preferences (adding part about lottery number and no other preferences just to further clarify the question). By the time Student A is being considered for school A, they have already not gotten spots at their 1st and 2nd choice schools.

Student B also has sibling preference at school A but ranked it #1. Student B's randomly assigned lottery number is 20. Student B has no other preferences.

Show me the official source that says either: "Student A will get the spot because their random lottery number is higher" or "Student B ranking school A will NOT give student B an advantage over Student A".

Don't just link, show the specific place where it is clearly stated/explained that Student A trumps B no matter what in this scenario.

First and foremost your example is flawed because it shows only 2 students and 3 schools. Demand for those seats isn't high enough to represent a true example... but I digress and will make this work by forcing Student 1's first and second choice schools to have zero seats offered in the lottery.

This is answered in the PDF that talks about gale/shapely. As a matter of fact a diagram exists that explains it.

Student A gets the spot because they have a higher lottery number and are therefore preferred by the school for that slot.

Here is the relevant diagram for your example:

Student Ranking Schools (based on true preference):
i1: sB, sC, sA
i2: sA, sB, sC

Schools Ranking Students (based on preference and lottery #):
sA: i1, i2
sB: no seats/preference
sC: no seats/preference

School A is the only school with seats in this lottery.
Now, when ranked purely by lottery number (and not preference) the students are sorted as i1, i2, i3. So i1 goes first.

i1 asks sB for a seat. sB says no. we move on to i2. i2 asks for sA. sA says yes. i1 then asks for sC. sC says no. i1 then asks for sA. sA sees that i1 is ranked higher than a student it previously accepted. it removes acceptance from the lowest ranked student (i2) and takes the seat back, giving it to i1. i2 then asks sB for a seat. sB says no. i2 then asks sC for a seat. sC says no.

This all happened because i1 had a better preference/lottery # combination. There are plenty of examples like this in the documents linked above.

[Anonymous]

Anonymous wrote:

Anonymous wrote:
We were arguing this point yesterday, but as of yesterday, who is disputing this part of it?

The part we are now disputing is this:
Same scenario as above EXCEPT Child #2 DOES have sibling preference. Who gets the spot then if both children have sibling preference but Child #1 ranked the school #3 and didn't get into 1-2, vs. Child #2 who ranked the school #1?

If you believe parent ranking has no effect beyond what order the computer tries to place you, you believe basically that at this point it's random. Those of us saying parent ranking matters are saying that in THIS scenario, Child #2 will get the spot. Hands down. And random computer assigned lottery number does not impact anything at this point.

From the FAQ:

FAQ wrote:
How does the My School DC common lottery work?
Student-school matches are based on the number of spaces at each school; sibling, proximity, and other preferences; and each student’s choices. (Through the My School DC common lottery, the six DCPS specialized high schools admit students based on specific criteria.)

When there are more students than spaces at a school, students who have a preference (such as a sibling preference) will be the first to be offered spaces. Then, random selection decides which other students will be offered spaces.

Students will be matched with no more than one school. My School DC will try to match each student with their 1st choice, then their 2nd choice, and so on through the student’s list.


What are preferences (sibling preference, proximity preference, in-boundary preference)?
Students may have a preference at one or more schools. Students with a preference at a particular school are offered space at that school before students who don’t have a preference. There are four types of preferences:

Sibling preference (DCPS and public charter schools). Your child will have a sibling preference at a school where a sibling is currently enrolled. Some schools also offer a preference in the lottery and/or on the waiting list to siblings of accepted students. For example, if you have two children applying to the same school this year and one is accepted, the school may offer a preference to the accepted child’s brother or sister. These preferences vary by school, so if you have questions, it’s best to contact the school. If your child is admitted with a sibling preference, be prepared to prove that your children are siblings when you enroll them. (DCPS specialized high schools do not offer a sibling preference.)

Proximity preference (DCPS only). Your child will receive a preference if he or she lives within a reasonable walking distance of a school. (DCPS high schools do not offer a proximity preference.)

In-boundary preference (DCPS PK3 and PK4 only). PK3 and PK4 students receive a preference at their in-boundary DCPS schools.

Adams-boundary preference (Oyster-Adams Bilingual School only). In 2007, John Quincy Adams Elementary School merged with Oyster Bilingual School. Students living in the boundary of the former Adams Elementary School get a preference when applying to Oyster-Adams.

1. If two students have the same preference, lottery number determines which one gets it.2. Ranking a school higher is not a preference.
3. In this scenario, the child with with the better lottery number gets the slot.

Where in the section from the website does it say that in the top situation, a random lottery number trumps preference? It says "Then, random selection decides which other students will be offered spaces". But it also says "Students will be matched with no more than one school. My School DC will try to match each student with their 1st choice, then their 2nd choice, and so on through the student’s list."

What I was TOLD is that in a situation where all else is equal (meaning preferences and no one got into a school they ranked better yet), it is not your random lottery number but your ranking of the school that will determine if you get it. If you both ranked the school 1, the lottery number will be the tie breaker. But if one student didn't rank 1 and all else is equal, they're not in the running against the student who ranked it 1. The algorithm is only looking to distinguish first/match first between those where all else is equal, including how they ranked the school.

Show me where it is clearly stated that random lottery number trumps student's ranking of the school and, where all else is equal except the student's rank of the school, a higher random lottery number trumps student's ranking of school?

[Anonymous]

Anonymous wrote:

Anonymous wrote:
We were arguing this point yesterday, but as of yesterday, who is disputing this part of it?

The part we are now disputing is this:
Same scenario as above EXCEPT Child #2 DOES have sibling preference. Who gets the spot then if both children have sibling preference but Child #1 ranked the school #3 and didn't get into 1-2, vs. Child #2 who ranked the school #1?

If you believe parent ranking has no effect beyond what order the computer tries to place you, you believe basically that at this point it's random. Those of us saying parent ranking matters are saying that in THIS scenario, Child #2 will get the spot. Hands down. And random computer assigned lottery number does not impact anything at this point.

From the FAQ:

FAQ wrote:
How does the My School DC common lottery work?
Student-school matches are based on the number of spaces at each school; sibling, proximity, and other preferences; and each student’s choices. (Through the My School DC common lottery, the six DCPS specialized high schools admit students based on specific criteria.)

When there are more students than spaces at a school, students who have a preference (such as a sibling preference) will be the first to be offered spaces. Then, random selection decides which other students will be offered spaces.
Students will be matched with no more than one school. My School DC will try to match each student with their 1st choice, then their 2nd choice, and so on through the student’s list.


What are preferences (sibling preference, proximity preference, in-boundary preference)?
Students may have a preference at one or more schools. Students with a preference at a particular school are offered space at that school before students who don’t have a preference. There are four types of preferences:

Sibling preference (DCPS and public charter schools). Your child will have a sibling preference at a school where a sibling is currently enrolled. Some schools also offer a preference in the lottery and/or on the waiting list to siblings of accepted students. For example, if you have two children applying to the same school this year and one is accepted, the school may offer a preference to the accepted child’s brother or sister. These preferences vary by school, so if you have questions, it’s best to contact the school. If your child is admitted with a sibling preference, be prepared to prove that your children are siblings when you enroll them. (DCPS specialized high schools do not offer a sibling preference.)

Proximity preference (DCPS only). Your child will receive a preference if he or she lives within a reasonable walking distance of a school. (DCPS high schools do not offer a proximity preference.)

In-boundary preference (DCPS PK3 and PK4 only). PK3 and PK4 students receive a preference at their in-boundary DCPS schools.

Adams-boundary preference (Oyster-Adams Bilingual School only). In 2007, John Quincy Adams Elementary School merged with Oyster Bilingual School. Students living in the boundary of the former Adams Elementary School get a preference when applying to Oyster-Adams.

1. If two students have the same preference, lottery number determines which one gets it.
2. Ranking a school higher is not a preference.
3. In this scenario, the child with with the better lottery number gets the slot.

Thank you. Folks, see the bolded above. The FAQ is clear. There is nothing, NOTHING, that states that ranking a school higher will give you more weight in the lottery.

::drops mic, exits forum::

[Anonymous]

Anonymous wrote:

Anonymous wrote:
I've reviewed most of those, including step 3. It amazes me that so many of you completely don't get that the specific example we're talking about is not outlined in Step 3. The example, for the zillionth time, is:

Student A has sibling preference at school A but ranked it #3. Student A's randomly assigned lottery number is 10. Student A has no other preferences (adding part about lottery number and no other preferences just to further clarify the question). By the time Student A is being considered for school A, they have already not gotten spots at their 1st and 2nd choice schools.

Student B also has sibling preference at school A but ranked it #1. Student B's randomly assigned lottery number is 20. Student B has no other preferences.

Show me the official source that says either: "Student A will get the spot because their random lottery number is higher" or "Student B ranking school A will NOT give student B an advantage over Student A".

Don't just link, show the specific place where it is clearly stated/explained that Student A trumps B no matter what in this scenario.

First and foremost your example is flawed because it shows only 2 students and 3 schools. Demand for those seats isn't high enough to represent a true example... but I digress and will make this work by forcing Student 1's first and second choice schools to have zero seats offered in the lottery.

This is answered in the PDF that talks about gale/shapely. As a matter of fact a diagram exists that explains it.

Student A gets the spot because they have a higher lottery number and are therefore preferred by the school for that slot.

Here is the relevant diagram for your example:

Student Ranking Schools (based on true preference):
i1: sB, sC, sA
i2: sA, sB, sC

Schools Ranking Students (based on preference and lottery #):
sA: i1, i2
sB: no seats/preference
sC: no seats/preference

School A is the only school with seats in this lottery.
Now, when ranked purely by lottery number (and not preference) the students are sorted as i1, i2, i3. So i1 goes first.

i1 asks sB for a seat. sB says no. we move on to i2. i2 asks for sA. sA says yes. i1 then asks for sC. sC says no. i1 then asks for sA. sA sees that i1 is ranked higher than a student it previously accepted. it removes acceptance from the lowest ranked student (i2) and takes the seat back, giving it to i1. i2 then asks sB for a seat. sB says no. i2 then asks sC for a seat. sC says no.

This all happened because i1 had a better preference/lottery # combination. There are plenty of examples like this in the documents linked above.

What does "i" mean in "i1 and i2"? And when this says "i1 asks SB for a seat", what does it mean that i "asks a student for a seat and the student says no"? How does the computer "ask a student for a seat" and how does the student "say no" in this year's DC common lottery process? Please break that down into plain terms, thanks.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:
I've reviewed most of those, including step 3. It amazes me that so many of you completely don't get that the specific example we're talking about is not outlined in Step 3. The example, for the zillionth time, is:

Student A has sibling preference at school A but ranked it #3. Student A's randomly assigned lottery number is 10. Student A has no other preferences (adding part about lottery number and no other preferences just to further clarify the question). By the time Student A is being considered for school A, they have already not gotten spots at their 1st and 2nd choice schools.

Student B also has sibling preference at school A but ranked it #1. Student B's randomly assigned lottery number is 20. Student B has no other preferences.

Show me the official source that says either: "Student A will get the spot because their random lottery number is higher" or "Student B ranking school A will NOT give student B an advantage over Student A".

Don't just link, show the specific place where it is clearly stated/explained that Student A trumps B no matter what in this scenario.

First and foremost your example is flawed because it shows only 2 students and 3 schools. Demand for those seats isn't high enough to represent a true example... but I digress and will make this work by forcing Student 1's first and second choice schools to have zero seats offered in the lottery.

This is answered in the PDF that talks about gale/shapely. As a matter of fact a diagram exists that explains it.

Student A gets the spot because they have a higher lottery number and are therefore preferred by the school for that slot.

Here is the relevant diagram for your example:

Student Ranking Schools (based on true preference):
i1: sB, sC, sA
i2: sA, sB, sC

Schools Ranking Students (based on preference and lottery #):
sA: i1, i2
sB: no seats/preference
sC: no seats/preference

School A is the only school with seats in this lottery.
Now, when ranked purely by lottery number (and not preference) the students are sorted as i1, i2, i3. So i1 goes first.

i1 asks sB for a seat. sB says no. we move on to i2. i2 asks for sA. sA says yes. i1 then asks for sC. sC says no. i1 then asks for sA. sA sees that i1 is ranked higher than a student it previously accepted. it removes acceptance from the lowest ranked student (i2) and takes the seat back, giving it to i1. i2 then asks sB for a seat. sB says no. i2 then asks sC for a seat. sC says no.

This all happened because i1 had a better preference/lottery # combination. There are plenty of examples like this in the documents linked above.

What does "i" mean in "i1 and i2"? And when this says "i1 asks SB for a seat", what does it mean that i "asks a student for a seat and the student says no"? How does the computer "ask a student for a seat" and how does the student "say no" in this year's DC common lottery process? Please break that down into plain terms, thanks.

Clarification - I assume "i" is the school, but you threw me with "i1 asks sB for a seat", so just making sure.

[Anonymous]

"i" is the student

"s" is the school

I thought that was clear by stating

Student Ranking Schools (based on true preference):
i1: sB, sC, sA
i2: sA, sB, sC

Schools Ranking Students (based on preference and lottery #):
sA: i1, i2
sB: no seats/preference
sC: no seats/preference

anything else that isn't clear?

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:
I've reviewed most of those, including step 3. It amazes me that so many of you completely don't get that the specific example we're talking about is not outlined in Step 3. The example, for the zillionth time, is:

Student A has sibling preference at school A but ranked it #3. Student A's randomly assigned lottery number is 10. Student A has no other preferences (adding part about lottery number and no other preferences just to further clarify the question). By the time Student A is being considered for school A, they have already not gotten spots at their 1st and 2nd choice schools.

Student B also has sibling preference at school A but ranked it #1. Student B's randomly assigned lottery number is 20. Student B has no other preferences.

Show me the official source that says either: "Student A will get the spot because their random lottery number is higher" or "Student B ranking school A will NOT give student B an advantage over Student A".

Don't just link, show the specific place where it is clearly stated/explained that Student A trumps B no matter what in this scenario.

First and foremost your example is flawed because it shows only 2 students and 3 schools. Demand for those seats isn't high enough to represent a true example... but I digress and will make this work by forcing Student 1's first and second choice schools to have zero seats offered in the lottery.

This is answered in the PDF that talks about gale/shapely. As a matter of fact a diagram exists that explains it.

Student A gets the spot because they have a higher lottery number and are therefore preferred by the school for that slot.

Here is the relevant diagram for your example:

Student Ranking Schools (based on true preference):
i1: sB, sC, sA
i2: sA, sB, sC

Schools Ranking Students (based on preference and lottery #):
sA: i1, i2
sB: no seats/preference
sC: no seats/preference

School A is the only school with seats in this lottery.
Now, when ranked purely by lottery number (and not preference) the students are sorted as i1, i2, i3. So i1 goes first.

i1 asks sB for a seat. sB says no. we move on to i2. i2 asks for sA. sA says yes. i1 then asks for sC. sC says no. i1 then asks for sA. sA sees that i1 is ranked higher than a student it previously accepted. it removes acceptance from the lowest ranked student (i2) and takes the seat back, giving it to i1. i2 then asks sB for a seat. sB says no. i2 then asks sC for a seat. sC says no.

This all happened because i1 had a better preference/lottery # combination. There are plenty of examples like this in the documents linked above.

What does "i" mean in "i1 and i2"? And when this says "i1 asks SB for a seat", what does it mean that i "asks a student for a seat and the student says no"? How does the computer "ask a student for a seat" and how does the student "say no" in this year's DC common lottery process? Please break that down into plain terms, thanks.

I am not the PP whom you are quoting, but basically the way it works is that in the algorithm, the computer model has the student "asks" for a seat to the school for their first choice. They are temporarily assigned a seat or rejected by the school (again, all done by computer--student doesn't actually ask someone at the school). Then the students who didn't get in during the prior round ask their next choice school, and the schools reconsider the people who got in the first round with the people who are asking in the second round based on the random lottery numbers and chooses schools. Then the people who no longer have seats after round 2 ask for their next choice school, etc. etc. Again, all done by computer based on the student's rankings (with those with clear preferences--IB, sib, etc. --going in first, then everyone else) along with the random lottery # order generated by the computer for the schools.