 A very common assumption is that a rational preference ordering must be transitive (i.e., if \(A\) is preferred to \(B\), and \(B\) is preferred to \(C\), then \(A\) must be preferred to \(C\)). See the entry on preferences (Hansson and Grüne-Yanoff 2009) for an extended discussion of the rationale behind this assumption. Indeed, if a voter’s preference ordering is not transitive, for instance, allowing for cycles (e.g., an ordering of \(A, B, C\) with  \(A \succ B \succ C \succ A\), where \(X\succ Y\) means \(X\) is strictly preferred to \(Y\)), then there is  no alternative that the voter can be said to actually support (for each alternative, there is another alternative that the voter strictly prefers). Many authors argue that voters with cyclic preference orderings have inconsistent opinions about the candidates and should be ignored by a voting method (in particular, Condorcet forcefully argued this point). A key observation of Condorcet (which has become known as the Condorcet Paradox) is that the majority ordering may have cycles (even when all the voters submit rankings of the alternatives). 