ℓ-Cohesive Voter Group (COMSOC)

Definition

ℓ-Cohesive Voter Group ( COMSOC)

Let $V$ be an electorate of $n=|V|$ voters, let $k$ be the committee size, and let $A_i\subseteq C$ be the approval set of each voter $v_i$.

A group $V^{\prime }\subseteq V$ is called $\ell$-cohesive voter group if

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