 Effectivity functions are closed under supersets, i.e., we have that \(X\in E(C)\) and \(X\subseteq Y \subseteq W\) imply that \(Y \in E(C)\). In other words, if \(X\) is within the power of coalition \(C\) then so is each of \(X\)’s supersets. From this, notice, it follows that if an effectivity function of a certain coalition is not empty then it always contains the set of all outcomes.  For \(\mathcal{X} \subseteq {2^{W}}\) we denote \(\mathcal{X}^{+}\) its superset closure.