Stable MarriageDating Scenario
There are n men and n women
Each woman has her own ranked preference list of all the men
Each man has his own ranked preference list of the women
The lists have no ties
1
2
3
4
5
3,2,5,1,4
1,2,5,3,4
4,3,2,1,5
1,3,4,2,5
1,2,4,5,3
1
2
3
4
5
3,5,2,1,4
5,2,1,4,3
4,3,5,1,2
1,2,3,4,5
2,3,4,1,5
Maximizing total satisfaction … ?
Suppose we match all the men and women
Now suppose that some man and some woman prefer each other to the people to whom they are matched
They are called a blocking pair
blocking pair
*
*
Why be with them when we can be with each other?
blocking pair
if it is not stable?
*
*
A matching of men and women is called stable if it contains no blocking pairs
Stable Matching
3,2,1
1
2,1,3
2
3,1,2
3
1
3,2,1
2
1,2,3
3
3,2,1
A matching of men and women is called stable if it contains no blocking pairs
Stable Matching
participate in the Main Residency Match. In addition, another
20,000 applicants complete for the approximately 25,000
available residency positions.
*
*