Finding stable sets of pairings: an example


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

Men's preferencesAnneElenaHeatherLaura
Andy1234
Colin1234
Jamie3124
Ross2314
Women's preferencesAndyColinJamieRoss
Anne3412
Elena2341
Heather1234
Laura3421

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 offersStage 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 offersStage 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 offersStage 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 offersStage 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 offersStage 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.

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