Give an example of a stable matching instance with $4$ riders and $4$ horses, with stable matchings M$1$ and M$2$ such that for some riders r$1$ and r$2$:

$$ r$1$ prefers their match in M$1$ to their match in M$2$

$$ r$2$ prefers their match in M$2$ to their match in M$1$

Note that this requires r$1$ and r$2$ both change partners between M$1$ and M$2.$

Hint: r$1$ and r$2$ might not be the only riders changing partners, and r$1$ and r$2$ may not simply be switching partners with each other.