 leading to a social preference for \(x\) over \(z\) over \(y\) over \(w\). The only difference between the two profiles lies in Individual 1’s preference ordering, and even here there is no change in the relative ranking of \(x\) and \(z\). Despite identical individual preferences between \(x\) and \(z\) in Tables 3 and 4, the social preference between \(x\) and \(z\) is reversed, a violation of independence of irrelevant alternatives.