Consider a legislature consisting of five legislators (A, B, C, D, E) with ideal points: xA = 1, xB = 2, xC = 3, xD = 4, xE = 5. The legislators have symmetric, single-peaked preferences (i.e. they always prefer policies closer to their ideal point). The status quo is Xsq = 1. Legislator E is the leader of the chamber (agenda setter) who can propose a new policy, x. After the leader proposes a policy, the legislature can accept or reject the proposal. If the proposed policy is rejected, the status quo remains in place. If the proposed policy is accepted, the new policy is implemented. All legislators (including the leader) vote on the proposal. (a) Suppose the legislature uses simple majority rule when they vote on new policy proposals (i.e. at least three out of five legislators need to vote in favor for the proposal to pass). What policy will the leader propose in equilibrium? Explain. (Hint: legislators C and D are effectively veto players since the leader, legislator E, needs their approval for her policy proposal to pass) (b) Suppose the legislature uses super majority rule when they vote on new policy proposals such that at least