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[quote=Anonymous][quote=Anonymous][quote=Anonymous]"i" is the student

"s" is the school

I thought that was clear by stating 
[quote]
[b]Student Ranking Schools (based on true preference): [/b]
i1: sB, sC, sA 
i2: sA, sB, sC

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

anything else that isn't clear?[/quote]

err.... all of it?  I don't usually have trouble following this kind of thing but your description is incomprehensible.[/quote]

There is another example in the thread that uses more language based terms to describe the process.

[quote]
It's quite complicated and quite simple:

[quote="This is how Gale/Shapley works from a logical approach"]

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. 
[/quote]

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.[/quote][/quote]

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