Introduction

We have been through a lengthy odyssey, more than a dozen case studies, each an island of terrors and delights. Now as we approach Ithaca it is time to recall why we started our journey. The Arrow theorem disclosed the logical possibility of a majority cycle, of perpetual political instability. But we observe stability rather than instability in democratic politics. Riker (1958) initially responds that cycles are common but rarely detected. Simulations show and empirical studies corroborate, however, that cycling is an empirical improbability. Riker then concedes that uncontrived cycles are quite rare, but that on major issues actors will contrive cycles by introduction of new alternatives. Actors also engage in strategic voting, agenda control, and the introduction of new dimensions in order to contrive multidimensional disequilibrium, according to Riker.

I object that he must show that manipulation is frequent, harmful, and irremediable. Riker's position is that it is either theoretically impossible or empirically difficult to detect such manipulation. He is able, however, to produce spectacular anecdotes that show harmful manipulation on major issues, including a demonstration that the biggest event in American history was the consequence of a contrived cycle. We have worked through each of his examples, only to find that each is mistaken, and thus Riker's case fails on its own terms. In summary, theoretical considerations about the distribution of preference orders suggest that cycles are most unlikely; empirical studies show that cycles are of no practical importance; finally, almost every developed and published example of a political cycle has now been refuted.