(Top cycle set) A committee has three members.
a. Suppose that there are three alternatives, x, y, and z, and that one member prefers x to y to z, another prefers y to z to x, and the third prefers z to x to y. Find the top cycle set.
b. Suppose that there are four alternatives, w, x, y, and z, and that one member prefers w to z to x to y, one member prefers y to w to z to x, and one member prefers x to y to w to z. Find the top cycle set. Show, in particular, that z is in the top cycle set even though all committee members prefer w.