Strong Neutrality (SN): For all alternatives \(x\), \(y\), \(z\) and \(w\), and all profiles \(\langle R_{i}\rangle\) and \(\langle R_{i}^*\rangle\): IF for all \(i\): \(xR_{i}y\) if and only if \(zR^*_{i}w\), and \(yR_{i}x\) if and only if \(wR^*_{i}z\), THEN \(x f\langle R_{i}\rangle y\) if and only if \(z f\langle R_{i}^*\rangle w\), and \(y f\langle R_{i}\rangle x\) if and only if \(w f\langle R_{i}^*\rangle z\).