Arrow’s independence condition requires that whenever all individual preferences among a pair of alternatives are the same in one profile as they are in another, the social preference among these alternatives must also be the same for the two profiles. Speaking figuratively, what this means is that when the social welfare function goes about the work of aggregating individual orderings, it has to take each pair of alternatives separately, paying no attention to preferences for alternatives other than them. Some aggregation procedures work this way. Pairwise majority decision does: it counts \(x\) as weakly preferred to \(y\), socially, if as many people weakly prefer \(x\) to \(y\) as the other way around, and plainly there is no need to look beyond \(x\) and \(y\) to find this out.