Abstract
The classical Gale-Shapley stable marriage algorithm produces a stable marriage that greatly favors one sex over the other. It is therefore of interest to find other stable marriages providing good compromises between the preferences of the two sexes. In this note we parametrically shift favor between the preferences of the men and the women, to define a continuum of possible compromises between the sexes. In two versions of the problem, we show that the number of stable marriages in this continuum is very small, and that these marriages can be found efficiently. The efficiency comes from generalizing a recent method by Gallo, Grigoriadis and Tarjan (1988) to compute parametric network flows.
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