Marriage matching and gender satisfaction |
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Authors: | Vicki Knoblauch |
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Institution: | (1) Department of Economics, University of Connecticut, Storrs, CT 06269-1063, USA |
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Abstract: | The performance of the Gale–Shapley marriage matching algorithm (Am Math Mon 16:217–222, 1962) has been studied extensively
in the special case of men’s and women’s preferences random. We drop the assumption that women’s preferences are random and
show that , where R
n
is the men’s expected level of satisfaction, that is, the expected sum of men’s rankings of their assigned mates, when the
men-propose Gale–Shapley algorithm is used to match n men with n women. This is a step towards establishing a conjecture of Knuth (Mariages Stables et leurs relations avec d’ autres problémes
combinatoires, 1976, CRM Proceedings and Lecture Notes, Vol 10, 1997) of 30 years standing. Under the same assumptions, we
also establish bounds on the expected rankings by women of their assigned mates. |
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Keywords: | |
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