In a particular instance of the stable marriage problem with n men and n women,

Question

In a particular instance of the stable marriage problem with n men and n women, it turns out that there are exactly three distinct stable matchings, M1, M2, M3. Also, each woman w has a different partner in the three matchings. Therefore each woman has a clear preference ordering of the three matchings (according to the ranking of her partners in her preference list). Now, suppose for woman w1, this order is M1 > M2 > M3. True or false: Every woman has the same preference ordering M1 > M2 > M3. Answer it and justify.

Explanation / Answer

Since every woman has her unique set of match preferences and different partner in each matching, hence this rules out the case of every woman having the same set of match preference. hence M1>M2<M3 cannot be the same preference ordering.

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