Consider a committee that consists of three people, A, B, and C, that is to examine three proposals, x, y, and z. The committee can adopt at most one of the three proposals; it also has the option of adopting none. The committee will first vote on x. If x receives at least two votes it will be adopted; if not, the committee will vote on y. If y receives at least two votes it will be adopted; if not, the committee will vote on z. If z receives at least two votes it will be adopted; if not, then none of the proposals will be adopted. The committee members' payoffs are as follows:

A B C

x 2 1 3

y 1 4 2

z 4 3 1

None 3 2 4

Every member of the committee knows everyone's preferences (e.g., A knows that B likes y best, z second best, and so on). Find the subgame perfect Nash equilibrium of this game.