Independence of Irrelevant Alternatives (I): For all alternatives \(x\) and \(y\) in \(X\), and all profiles \(\langle G_{i}\rangle\) and \(\langle G^*_{i}\rangle\) in the domain of \(f\), if \(\langle G_{i}\rangle|\{x,y\} = \langle G^*_{i}\rangle|\{x,y\}\), then \(f\langle G_{i}\rangle |\{x,y\} = f\langle G^*_{i}\rangle |\{x,y\}\).