February 9, 2013

searching for a stable marriage

Over new years, a bunch of my closest friends came to visit.
And as we do, we caught each other up about the goings on of our lives.
I was telling one of my mathematician friends about interviewing for Residency.
As I took a deep breath before launching into what had become my "elevator talk" of how the Matching process works, she said to me, oh I know how that works.  It's a well-known mathematical theorem for which Gale won the Nobel Prize.  
But in math, it's called "The Stable Marriage Problem"

She explained it simply and eloquently to me at the time, but I have since been shown the following video which breaks it down on a chalkboard (!!)
even to the point of explaining how matching as a couple is a little bit "off algorithm".
as someone whose life course will be forever changed by this algorithm, I figured I best at least try to understand it.  If you don't have the luxury of talking with brilliant friends who are mathematicians, check out the video below.  

(it's fascinating even if you are not interested in math or residency)

the central theorems she reviews in this video are:
0. this algorithm terminates (as in, stable marriages are possible for everyone!)
1. the marriages are stable (meaning, no one would rather have someone else who would also rather have them)
2. all men ("applicants") are simultaneously matched to their best mate
3. all women ("programs") are matched to their worst mate (but it's still a match, and that doesn't mean it's not also their first choice)

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