Given how women initiate most divorces, it's probably best to set it up so they are the proposing side.
But this isn't raw Gale-Shapley-- the participants aren't ranking all hundreds/thousands of others. In particular, the preference matrix is based on identical mutual compatibility scores, so there's a unique stable solution (not multiple stable ones!), and there's no "side" that benefits, since the solution is identical no matter who does the "proposing".
But this isn't raw Gale-Shapley-- the participants aren't ranking all hundreds/thousands of others. In particular, the preference matrix is based on identical mutual compatibility scores, so there's a unique stable solution (not multiple stable ones!), and there's no "side" that benefits, since the solution is identical no matter who does the "proposing".