Clarification request
"At the end, it is not possible for a man and a woman (call them Alice and Bob) to both prefer each other to their current partners."
What the heck does "both prefer each other to their current partners" mean? Aren't they 'currently their current partners' in the end? That doesn't seem like good english to me :[
It means that while Bob may have prefered Alice, Alice prefers her current partner to Bob. Or Alice may have preferred Bob, but Bob prefers his current partner. You can't have Bob preferring Alice to his current partner and Alice perferring Bob to her current partner.
Remember that Alice and Bob are NOT partners.