Cohesive Voter Group (COMSOC)

Definition

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 a cohesive voter group if

$$|V^{\prime }|\ge \frac{|V|}{k}\text{and}\bigcap _{v_i\in V^{\prime }}{A}_i\ne \varnothing .$$

Thus, $V^{\prime }$ contains enough voters to justify one of the $k$ committee seats and all voters in $V^{\prime }$ approve at least one common alternative.