 Transitivity means that if the agent prefers an element A to an element B and she prefers the element B to a third element C, then she prefers element A to element C. Many, but not all, relations are transitive. The relation “friends with,” for example, is not transitive as A may be friends with B and B may be friends with C while A and C mutually detest each other. The two conditions are thus minimal though not empty. 