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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]
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.[/quote]

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.[/quote]

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.[/quote]

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.[/quote]

Right, that would make sense.  But the example above does not have students asking the school for a seat, it says the school asks the student for a seat.  And the student says no!  What does that mean, the way the other poster wrote it?[/quote]

I think the PP probably meant the other way round--the student "proposes" to the school. However, the algorithm can be set up either way -- with the school "proposing" to the student or the student "proposing" to the school. Statistically, however, who does the proposing makes a difference to the outcomes--whichever side proposes gets better outcomes. So it is almost certain that the students will ask the schools and not vice versa, since that will maximize student welfare, the goal of the system. (You could maximize school welfare, but since the order for schools, within the preference tiers, is assigned by random lottery number, there is no real benefit to maximizing the schools' welfare--i.e., the schools don't really prefer one student over another for those who have no preference; the lottery number is just a way to select students.)

Sorry, I am a stats/economic geek. This is probably way TMI.[/quote]

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