That is, person 1 prefers \(A\) to \(B\), prefers \(B\) to \(C\), and prefers \(A\) to \(C\); person 2 prefers \(B\) to \(C\), and so on. Now, we might hope somehow to arrive at a single “social” ordering of the alternatives that reflects the preferences of all three. Then we could choose whichever alternative is, socially, best—or, if there is a tie for first place, we could choose some alternative that is as good as any other. Suppose, taking the alternatives pair by pair, we put the matter to a vote: we count one alternative as socially preferred to another if there are more voters who prefer it than there are who prefer the other one. We determine in this way that \(A\) is socially preferred to \(B\), since two voters (1 and 3) prefer \(A\) to \(B\), but only one (voter 2) prefers \(B\) to \(A\). Similarly, there is a social preference for \(B\) to \(C\). We might therefore expect to find that \(A\) is socially preferred to \(C\). By this reckoning, though, it is just the other way around, since there are two voters who prefer \(C\) to \(A\). We do not have a social ordering of the alternatives at all. We have a cycle. Starting from any alternative, moving to a socially preferred one, and from there to the next, you soon find yourself back where you  started.[1]