 A useful illustration of this idea involves an extension of majority rule to cases of more than two alternatives. The Condorcet rule says that an alternative x wins when, for every other alternative, a majority prefers x over that alternative. For example, suppose we have three persons A, B and C and three alternatives x, y and z. A prefers x over y, y over z; B prefers y over z and z over x; C prefers x over z and z over y. In this case, x is the Condorcet winner since it beats y, and it beats z. The problem with this plausible sounding rule is the case of a majority cycle. Suppose you have three persons A, B and C, and three alternatives, x, y and z. In the case in which A prefers x over y and y over z, while B prefers y over z and z over x, and C prefers z over x and x over y, the Condorcet rule will yield a social preference of x over y, y over z and z over x. One can see here that the Condorcet rule satisfies all the conditions except transitivity of social preference. One way to avoid intransitivity is to restrict the domain of preferences from which the social preference arises. Another is to introduce cardinal information that compares the how much people prefer alternatives (violating independence). Another might be to make one person a dictator. So, this case nicely illustrates that one cannot satisfy all of the constraints simultaneously.