#### Political science

- Suppose there are five members of a committee (A, B, C, D, and E), each with ideal points spread evenly along a unidimensional policy space. Suppose the status quo is at A’s ideal point, and that committee members may propose their ideal points in the following order: E, C, A. In other words, the first vote is between the status quo and E, the second vote is between the winner of the first vote and C, and so on. Assume votes are decided by majority rule and committee members vote for the proposal closest to their own ideal points. Where will policy be at the end of the agenda?

HINTS: If the status quo and the proposal are equidistant, the committee member votes for the status quo. If the proposal wins, it becomes the new status quo.

- Considering the same committee as above, suppose now that the status quo is at D, and that the agenda is: C, D, A. Where will policy be at the end of the agenda?

- Considering the same committee as above, suppose now that the all votes are under supermajority rule, and that a proposal must garner at least 4 of the 5 votes to win. Suppose the status quo is at A and the agenda is: E, C, A. Where will policy be at the end of the agenda?

- Consider the same committee as above, under the same supermajority rule. Suppose the status quo is at D, and the agenda is: C, D, A. Where will policy be at the end of the agenda?

- How do your answers to questions 1-4 relate to the median voter result, particularly with respect to the effect on the result of agenda control and supermajority requirements?

- Each figure below shows the ideal point of the median member of the House (
*H*), ideal point of the median member of the Senate (*S*), and a status quo (*Q*). In each figure, draw the win set against the status quo for the House median,*W**H**(Q)*, the win set against the status quo for the Senate median,*W**S**(Q)*, and the overall win set against the status quo*W(Q)*(*i.e.*, indicate the set of policies that could defeat the status quo).

H

S

Q

Q

S

H

S

Q

H

- Assume there are three legislators who rank three alternatives, X, Y, and Z, as follows:

Legislator 1: X > Y > Z

Legislator 2: Y > Z > X

Legislator 3: Z > X > Y

- Assume the rules of the legislature specify that the first vote will be between X and Y, with the wining motion then put against Z. If the legislators vote sincerely, what is the outcome? What if they all vote strategically? (show your work)

- Now assume the rules specify that the first vote will be between X and Z, with the winning motion put against Y. What are the sincere and strategic outcomes? (show your work)

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