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Assume that the ranking lists of all women by the men are the same, and analogously, the ranking of all men by the women are

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Assume that the ranking lists of all women by the men are the same, and analogously, the ranking of all men by the women are the same. In other words, there is a consensus between the women who is the most favorite man, the second favorite man and so on. Prove that then there is only one stable matching. What is it? (note that in general, the TMA finds one of possible multiple stable matchings)

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