Download Chapter 2 Test Review

Chapter 2 Test Review
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) The total number of votes in the weighted voting system 34 : 10, 7, 4, 4, 3, 3, 3, 1, 1 is
A) 36.
B) 9.
C) 10.
D) 34.
E) None of the above
1)
2) In the weighted voting system 9 : 11, 4, 2 ,
A) there are no dictators.
B) P1 has veto power but is not a dictator.
C) P1 is a dictator.
2)
3) In the weighted voting system q : 20, 19, 16, 2, 1, 1 , a two-thirds majority of the votes is needed to
pass a motion. The value of the quota q is
A) 59.
B) 7.
C) 20.
D) 40.
E) None of the above
3)
4) In the weighted voting system [30 : 24, 12, 8, 4, 2], the minimum percentage of votes needed to pass
a motion is
A) 50%.
B) 61%.
C) 60%.
D) 30%.
E) 51%.
4)
5) In the weighted voting system [q : 24, 12, 8, 4, 2], what is the smallest possible value of the quota q
for which P4 and P5 are dummies?
5)
6) In the weighted voting system 21 : 10, 8, 5, 3, 2 , the total number of possible sequential coalitions
involving all five players is
A) 16.
B) 120.
C) 24.
D) 720.
E) None of the above
6)
D) every player is a dictator.
E) None of the above
A) 24
B) 27
C) 31
D) 29
E) None of the above
1
Refer to the weighted voting system 35 : 32, 15, 10, 3 and the Banzhaf definition of power. (The four players are P1 , P2 ,
P3, and P4 .)
7) The weight of the coalition {P2 , P3 , P4 } is
7)
8) The number of winning coalitions is
A) 7.
B) 15.
C) 8.
D) 24.
E) None of the above
8)
9) Which players in the coalition {P1 , P3} are critical?
9)
A) 57.
B) 25.
C) 60.
D) 28.
E) None of the above
A) P1 and P3
B) None of the players
C) P1 only
D) P3 only
E) None of the above
10) The Banzhaf power distribution of the weighted voting system is
1
1
1
A) P1: 75%; P2 : 8 %; P3: 8 %; P4: 8 %.
3
3
3
10)
B) P1: 40%; P2 : 20%; P3: 20%; P4: 20%.
C) P1: 70%; P2 : 10%; P3: 10%; P4: 10%.
D) P1: 60%; P2 : 20%; P3: 10%; P4: 10%.
E) None of the above
Refer to the weighted voting system 8: 6, 3, 2 and the Shapley-Shubik definition of power. (The three players are P1, P2 ,
and P3 .)
11) Which player in the sequential coalition P1 , P2, P3 is pivotal?
A) P2
11)
12) In how many sequential coalitions is P2 the pivotal player?
12)
B) P3
C) P1
D) All three players
E) None of the above
A) 2
B) 0
C) 6
D) 1
E) None of the above
2
13) The Shapley-Shubik power distribution of the weighted voting system is
1
1
1
A) P1: ; P2 : ; P3: .
3
3
3
B) P1:
13)
2
1
1
;P : ;P : .
3 2 6 3 6
1
1
1
C) P1: ; P2 : ; P3: .
2
3
6
1
1
D) P1: ; P2 : ; P3: 0.
2
2
E) None of the above
Refer to the weighted voting system 25 : 16, 9, 9, 7 and the Banzhaf definition of power. (The four players are P1, P2, P3
and P4 .)
14) The weight of the coalition {P1 , P3 , P4 } is
14)
15) Which players are critical in the coalition {P1 , P3 , P4}?
15)
A) 41.
B) 43.
C) 32.
D) 25.
E) None of the above
A) All three players
B) P1 only
C) None of the players
D) P1 and P3 only
E) None of the above
16) Which players are critical in the coalition {P1 , P2 , P3, P4 }?
16)
A) All of the players
B) P1, P2 , and P3 only
C) P1 and P2 only
D) P1 only
E) None of the players
17) In this weighted voting system, which players have veto power?
A) P1 and P2 only
17)
B) All of the players
C) P1, P2 , and P3 only
D) P1 only
E) None of the players
18) The winning coalitions are:
A) all coalitions with two or more players.
B) all coalitions with P1 in it.
18)
C) all coalitions with three or more players.
D) {P1, P2 }, {P1, P3}, and all coalitions with three or more players.
E) None of the above
3
19) The number of winning coalitions is
A) 8.
B) 7.
C) 15.
D) 5.
E) None of the above
19)
20) The Banzhaf power distribution of the weighted voting system is
7
1
1
1
A) P1: ; P2: ; P3 : ; P4: .
12
6
6
12
20)
1
1
1
1
B) P1: ; P2 : ; P3: ; P4 : .
2
5
5
10
5
1
1
1
C) P1: ; P2: ; P3 : ; P4: .
12
4
4
12
1
1
1
1
D) P1: ; P2 : ; P3: ; P4 : .
3
4
4
6
E) None of the above
Solve the problem.
200!
=
21)
198!
21)
A) 200
B) 39,800
C) 399
D) 2
E) None of the above
22) 300! - 299! =
A) 299 × 299!
B) 300 - 2 × 299!
C) 1
D) 2992 × 298!
E) None of the above
22)
4