ℓ-Justified Representation (COMSOC)

Definition

ℓ- justified representation (COMSOC)

Let $\ell \in [k]$. A committee $C^{\ast }$ satisfies $\ell$-justified representation if for each voter group $V^{\prime }\subseteq V$ with

$$|V^{\prime }|\ge \ell \cdot \frac{n}{k}\text{and}\left|\bigcap _{v_i\in V^{\prime }}{A}_i\right|\ge \ell ,$$

there exists a voter $v_i\in V^{\prime }$ such that

$$|C^{\ast }\cap A_i|\ge \ell .$$