An altimeter for Mr. Escher’s stairway

Abstract

William Riker’s article explains a central thesis of social choice theory with its author’s characteristic vigor. The initial notion, first put forward some 195 years ago in Condorcet’s Essai (1785) is this: Given three or more alternatives (say laws or candidates and three of more voters, majorities may march in circles even while individuals do not. The contemporary literature presents an essentially two-sided extension of Condorcet’ little discovery: (i) that the condorcet paradox can be avoided only at cost of violating some other reasonable-sounding axioms for social choice (viz., Arrow’s theorem), and (ii) that under majority rule itsel, cyclic majorities will be common, often large, generally without a single alternative immune to the process of cyclic dominance. This second range of findings , built up by kramer, plott, Fishburn, Bell, McKelvey, Schofield, and many others, tell us that the Condorcet paradox is no fluke, and therefore is not the dismissible “phantom” which Gordon Tullock used to make it out to be. It must be integrated with, not banished from, our understanding of politicaltheory. This is what Riker tell us, and I agree. The question is to see why we should care about transitive consistency in liberal democratic (or any other) political theory.

The real world of values is inconsistent; that is to say, it is made up of antagonistic elements. To grant them full recognition simultaneously is impossible, yet each demands total acceptance. This is not a matter of logical contradictions, because values are not theoretical theses. It is a contradiction which lies at the heart of human behavior.

— Leszek Kolakowski (1968, p. 216)

Politics is the dismal science because we have learned from it that there are no equilibria to predict. In the absence of equilibria we cannot know much about the future at all, whether it is likely to be palatable or unpalatable, and in that sense our future is subject to the tricks and accidents of the way. alternatives are offered and eliminated.

-William H. Riker (1980a, p. 443)