# Finding stable sets of pairings: an example

The following is an example with four men and four women.

 Men's preferences Anne Elena Heather Laura Andy 1 2 3 4 Colin 1 2 3 4 Jamie 3 1 2 4 Ross 2 3 1 4
 Women's preferences Andy Colin Jamie Ross Anne 3 4 1 2 Elena 2 3 4 1 Heather 1 2 3 4 Laura 3 4 2 1

In the stages below "Woman: (x)Man(y)" indicates that the woman's rating of the man is x and the man's rating of the woman is y. So Anne: (3)Andy(1) means that Anne has rated Andy as 3rd on her list and Andy has rated Anne as 1st on his list.

 Stage 1 offers Stage 2 offers Anne: (3)Andy(1), (4)Colin(1) Elena: (4)Jamie(1) Heather: (4)Ross(1) Laura: Anne: (3)Andy(1) Elena: (4)Jamie(1), (3)Colin(2) Heather: (4)Ross(1) Laura: Anne turns Colin down. He goes to his next choice, Elena. Elena turns Jamie down. He goes to his next choice, Heather.
 Stage 3 offers Stage 4 offers Anne: (3)Andy(1) Elena: (3)Colin(2) Heather: (4)Ross(1), (3)Jamie(2) Laura: Anne: (3)Andy(1), (2)Ross(2) Elena: (3)Colin(2) Heather: (3)Jamie(2) Laura: Heather turns Ross down. He goes to his next choice, Anne. Anne turns Andy down. He goes to his next choice, Elena.
 Stage 5 offers Stage 6 offers Anne: (2)Ross(2) Elena: (3)Colin(2), (2)Andy(2) Heather: (3)Jamie(2) Laura: Anne: (2)Ross(2) Elena: (2)Andy(2) Heather: (3)Jamie(2), (2)Colin(3) Laura: Elena turns Colin down. He goes to his next choice, Heather. Heather turns Jamie down. He goes to his next choice, Anne.
 Stage 7 offers Stage 8 offers Anne: (2)Ross(2), (1)Jamie(3) Elena: (2)Andy(2) Heather: (2)Colin(3) Laura: Anne: (1)Jamie(3) Elena: (2)Andy(2), (1)Ross(3) Heather: (2)Colin(3) Laura: Anne turns Ross down. He goes to his next choice, Elena. Elena turns Andy down. He goes to his next choice, Heather.
 Stage 9 offers Stage 10 offers Anne: (1)Jamie(3) Elena: (1)Ross(3) Heather: (2)Colin(3), (1)Andy(3) Laura: Anne: (1)Jamie(3) Elena: (1)Ross(3) Heather: (1)Andy(3) Laura: (4)Colin(4) Heather turns Colin down. He goes to his next choice, Laura. All women have received offers; the process is complete.

Back to main article