I will first restate the question as I understand it after the clarifying comment. If I'm misunderstanding something, please let me know.
Let $M$ be a set of size $n$. There are two parties $A$ and $B$.
We are looking for a protocol that does the following.
$A$ chooses a subset $N\subseteq M$ with $|N|=2n/3$ and computes some message $m$ with $|m|=\ell$, ...