One lesson of the Paradox of Voting is that social-choice procedures sometimes flout social rationality: they do not fulfill the conditions of rationality long assumed for individual choice. The rough idea is that a rational individual always makes a most preferred choice, but a society cannot when the social preference is cyclic. In a way, Arrow’s celebrated Impossibility Theorem generalizes this lesson—but not the Paradox of Voting, as is too often alleged. It does show that certain modest assumptions force a breakdown in the transitivity of either social preference or social indifference, the beat or tie relation, but that is consistent with the absence of cycles. Even so, Arrow’s Theorem can be turned into a generalization of the Paradox of Voting. For we can add a bit to his assumptions and get a cycle. The next chapter shows how.