 Note that the Gale-Shapley matching algorithm is hugely favourable to the party that is doing the proposing. The proposing party gets a chance to make proposals to any candidate, in order of preference. But at the start of the procedure the receiving party has to say “yes” to any proposal! The result of swapping the roles of the men and the women in the algorithm will also compute a stable match, but one that is more advantageous to the women. 