Friday, July 16, 2010
Dubi Samet has a paper on stable marriage, explaining why you might have married as well as you did, and explaining how, when there is substantial agreement on rankings, you and your spouse can't have done too differently well.
(I conclude that if, like me, you "married up" it is because your spouse has contrarian tastes.)
"Abstract: When men and women are objectively ranked in a marriage problem, say by beauty, then pairing individuals of equal rank is the only stable matching. We generalize this observation by providing bounds on the size of the rank gap between mates in a stable matchings in terms of the size of the ranking sets. Using a metric on the set of matchings, we provide bounds on the diameter of the core---the set of stable matchings---in terms of the size of the ranking sets and in terms of the size of the rank gap. We conclude that when the set of rankings is small, so are the core and the rank gap in stable matchings."