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In 1962, David Gale and Lloyd Shapley proved that, for any equal number of men and women, and each man and each woman give a strict order of preference to the opposite sex, they can always solve for at least one stable marriage solution. What they didn't tell us is how to find all stable solutions. In this paper, I will demonstrate how to find every stable solution to a stable marriage problem. And I will discover the expected number of the stable matching for the stable marriage problem. Moreover, I will use the scoring system to quantify how much a man or a woman prefer the opposite sex, denoted as ``happiness score''. Then we can use the scoring system to present every matching on the $xy$-plane and look at the distribution of matchings.
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Chang, Chenyu, "Investigations of finding all stable solutions of Stable Marriage Problem" (2019). Senior Projects Spring 2019. 288.
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