Cycling and majority rule is one of the most heavily researched areas of public choice. The literature on this subject dates back to Condorcet (1785), who discovered the famous three-voter, three-alternative example of cyclical majorities so well known to public choice theorists, in which one majority prefers an alternative A to an alternative B, another majority prefers B to alternative C, and a third majority prefers C to A. Dodgson (1876) rediscovered this paradox in the nineteenth century, but serious investigation of this area begins with Black (1958) and Arrow (1951). In the last half of the twentieth century, the literature on cycling and majority rule has become quite extensive. Cycles are considered a defect in majority rule and the question most frequently asked is how they can be avoided. More precisely, scholars have sought conditions sufficient and/or necessary for the existence of an alternative that cannot be defeated by any other alternative in a majority contest. Such an alternative is known as an undominated point. Though an undominated point does not preclude the existence of a cycle among other alternatives, the type of cycle that concerns most theorists is what Schwartz (1986) calls a “top cycle,” one that leaves no alternative unbeatable.
Of course, the full transitivity of the majority preference relation means that an undominated point exists, but this requirement is stricter than necessary for the existence of an undominated point.