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.