You’re absolutely right. I’m on my phone trying to imagine the scenarios in my head and trying to find the simplest possible example.
Maybe 4 participants is too few to clearly see what happens.
Maybe 4 participants is too few to clearly see what happens.
The minimal example with 4 participants is if each person P has unique preferences and P's 1st choice has P as 2nd choice. So in this case just flip X:
A:XY B:YX X:BA Y:AB
If A,B propose you get AX,BY. If X,Y propose you get BX,AY. Both are stable because the proposers are getting their first choice.
This obviously doesn't factor in most of the complexity of romantic relationships: not knowing your own preferences, evolving preferences, incomplete/imperfect information in general, etc. Plus it assumes a global 1:1 matching across two categories, and people can of course be LGBT or choose to be single.