# Veto Player Games

Questions 1–6

Assume a bicameral legislature and a one-dimensional left-right policy space stretching from 0 to 10. The location of the status quo policy is SQ = 5, the location of the me- dian voter in the lower chamber is LC = 9, and the location of the median voter in the upper chamber is UC = 7. Assume that both median voters have a single-peaked utility function and that the support of both chambers is needed to pass a new policy. Assume that a voter will vote for a new policy over the status quo if she is indifferent between them.

(1) What is the range of policies that the median voter in the lower chamber prefers to the status quo?

? (a) 5-10.

? (b) 5-9.

? (c) 5-7.

? (d) 7-9.

? (e) 4-10.

(2) What is the range of policies that the median voter in the upper chamber prefers to the status quo?

? (a) 5-10.

? (b) 5-9.

? (c) 5-7.

? (d) 7-9.

? (e) 4-10.

(3) What is the overlapping range of policies preferred by both chambers to the status quo?

? (a) 5-10.

? (b) 5-9.

? (c) 5-7.

? (d) 7-9.

? (e) 4-10.

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(4) If the lower chamber is the agenda setter and can make take-it-or-leave-it proposals, where on the left-right issue dimension will the lower chamber make its policy proposal?

? (a) 5.

? (b) 7.

? (c) 8.

? (d) 9.

? (e) 10.

(5) If the upper chamber is the agenda setter and can make take-it-or-leave-it proposals, where on the left-right issue dimension will the upper chamber make its policy proposal?

? (a) 5.

? (b) 7.

? (c) 8.

? (d) 9.

? (e) 10.

(6) Now assume that SQ = 8. What is the winset of the status quo?

? (a) The winset is empty.

? (b) 7-8.

? (c) 8-9.

? (d) 7-9.

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Questions 7–9

Figures 1 and 2 on the next page show a two-dimensional issue space, where both social spending and defense spending can range from 1 to 5. The status quo (SQ) policy and the ideal points of veto players A and B are shown. For now there is no agenda setter.

(7) Would you expect defense policy to be more stable in Figure 1 or in Figure 2?

? (a) More stable in Figure 1.

? (b) More stable in Figure 2.

? (c) The same in both figures.

(8) Would you expect the size of a defense policy shift to differ in Figures 1 and 2?

? (a) Bigger in Figure 1.

? (b) Bigger in Figure 2.

? (c) The same in both figures.

(9) Now assume that player A is the agenda setter in both figures. Is player A more powerful in Figure 1 or in Figure 2?

? (a) More powerful in Figure 1.

? (b) More powerful in Figure 2.

? (c) Equally powerful in both figures.

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Figure 1:

1 2 3 4 5

1 2

3 4

5

Social spending

D e fe

n s e s

p e n d in

g

SQ

A

B

Figure 2:

1 2 3 4 5

1 2

3 4

5

Social spending

D e fe

n s e s

p e n d in

g

SQ

A B

5

Questions 10–11

Figure 3 on the next page shows a two-dimensional issue space. The status quo (SQ) policy and the ideal points of veto players A and B are shown. Potential policy proposals are denoted by X.

(10) Draw indifference curves for each veto player with respect to the status quo (SQ). Shade in the winset if there is one. Which of the potential policy proposals (labeled X1- X5) would win in a pairwise contest against the status quo?

? (a) X1.

? (b) X2.

? (c) X3.

? (d) X4.

? (e) X5.

? (f) None of them is located within the winset.

(11) If Figure 3 remained the same except that B were no longer a veto player — that is, if A could choose policy independently — where would policy end up?

? (a) X1.

? (b) X2.

? (c) X3.

? (d) X4.

? (e) X5.

? (f) A.

? (g) B.

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Figure 3:

1 2 3 4 5

1 2

3 4

5

Two veto players A and B

Issue 1

Is su

e 2

SQ

A

B

X1

X2 X3

X4

X5

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Question 12

Figure 4 on the next page shows a two-dimensional issue space. The status quo (SQ) policy and the ideal points of veto players A, B, and C are shown. Potential policy proposals are denoted by X.

(12) Draw indifference curves for each veto player with respect to the status quo (SQ). Shade in the winset if there is one. Which of the potential policy proposals (labeled X1- X5) would win in a pairwise contest against the status quo?

? (a) X1.

? (b) X2.

? (c) X3.

? (d) X4.

? (e) X5.

? (f) None of them is located within the winset.

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Figure 4:

1 2 3 4 5

1 2

3 4

5

Three veto players A, B, and C

Issue 1

Is su

e 2

SQ

A

B

C

X1

X2 X3

X4

X5

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