Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) In the weighted voting system
,
A) there are no dictators.
B) has veto power but is not a dictator.
C) every player is a dictator.
D) is a dictator.
E) none of these
2) In the weighted voting system
,
A) has veto power but is not a dictator.
B) every player is a dictator.
C) is a dictator.
D) there are no dictators
E) none of these
3) In the weighted voting system
A)
and
,
have equal power,
is a dummy.
B) and have equal power, is not a dummy.
C) all three players have equal power.
D) has all the power,
E) none of these
and
4) In the weighted voting system
are dummies.
,
A) has veto power, is a dummy.
B) all three players have veto power.
C) and have veto power,
D) no player has veto power.
E) none of these
5) In the weighted voting system
quota q is
is a dummy.
, a strict majority of the votes is needed to pass a motion. The value of the
A) 13.
B) 11.
C) 12.
D) 10.
E) none of these
1
6) In the weighted voting system
A) no player has veto power.
,
B) and have veto power, is a dummy.
C) all three players have veto power.
D) only has veto power.
E) none of these
7) In the weighted voting system
quota q is
, a strict majority of the votes is needed to pass a motion. The value of the
A) 12.
B) 10.
C) 11.
D) 13.
E) none of these
8) In the weighted voting system
value of the quota q is
, a two-thirds majority of the votes is needed to pass a motion. The
A) 7.
B) 40.
C) 20.
D) 59.
E) none of these
9) In the weighted voting system
, the largest possible value that the quota q can take is
A) 15.
B) 29.
C) 22.
D) 30.
E) none of these
10) In the weighted voting system
, the smallest possible value that the quota q can take is
A) 36.
B) 24.
C) 25.
D) 50.
E) none of these
11) In the weighted voting system [q : 24, 12, 8, 4, 2], what is the smallest possible value of the quota q for which
dummy?
A) 27
B) 29
C) 24
D) 30
E) none of these
is a
2
12) In the weighted voting system [30 : 24, 12, 8, 4, 2], the minimum percentage of votes needed to pass a motion is
A) 30%.
B) 61%.
C) 51%.
D) 50%.
E) 60%.
13) In the weighted voting system
A) 13.
B) 11.
C) 23.
D) 12.
E) none of these
, the smallest possible value that the quota q can take is
14) In the weighted voting system [q : 24, 12, 8, 4, 2], what is the smallest possible value of the quota q for which
and
are dummies?
A) 27
B) 29
C) 24
D) 31
E) none of these
15) In the weighted voting system [q : 24, 12, 6, 3], what is the largest possible value of the quota q for which
dummy?
is a
A) 42
B) 39
C) 41
D) 40
E) none of these
16) In the weighted voting system
, every player has veto power. The value of the quota q is
A) 11.
B) 20.
C) 22.
D) 21.
E) none of these
3
17) In the weighted voting system
can take is
, no player has veto power. The largest possible value that the quota q
A) 11.
B) 17.
C) 10.
D) 9.
E) none of these
18) A board is made up of two women (W) and three men (M). In order to pass a motion, three of the five including at
least one woman must vote "yes". Which of the following weighted voting systems represent this situation?
A) [8 : 3, 3, 2, 2, 2]
B) [7 : 3, 3, 2, 2, 2]
C) [6 : 3, 3, 2, 2, 2]
D) [3 : 1, 1, 1, 1, 1]
E) none of these
A committee consists of six members (A, B, C, D, E, and F). A has veto power; B, C, D, and E each have one vote. F is a
nonvoting member. For a motion to pass it must have the support of A plus at least two additional voting members.
19) A weighted system that could represent this situation is
A) [5 : 3, 1, 1, 1, 1, 0].
B) [6 : 5, 1, 1, 1, 1, 0].
C) [4 : 2, 1, 1, 1, 1, 0].
D) [6 : 3, 1, 1, 1, 1, 0].
E) none of these
Solve the problem.
20) In the weighted voting system
q can take is
, no player has veto power. The largest possible value that the quota
A) 17.
B) 11.
C) 13.
D) 15.
E) none of these
21) In the weighted voting system
, every player has veto power. The value of the quota q is
A) 15.
B) 17.
C) 18.
D) 10.
E) none of these
4
22) What is the largest value of w for which
is not a dummy in the weighted voting system
A) 1
B) 5
C) 3
D) 6
E) none of these
23) In the weighted voting system
, the smallest possible value that the quota q can take is
A) 12.
B) 29.
C) 15.
D) 14.
E) none of these
24) In the weighted voting system
value of the quota q is
, a two-thirds majority of the votes is needed to pass a motion. The
A) 7.
B) 29.
C) 20.
D) 19.
E) none of these
25) In the weighted voting system
A) all three players have equal power.
,
B)
and
have equal power,
is a dummy.
C)
and
have equal power,
is not a dummy.
D) has all the power,
E) none of these
and
26) In the weighted voting system
are dummies.
,
A) is a dictator.
B) no player has veto power.
C) every player has veto power.
D) has veto power but is not a dictator.
E) none of these
5
1) D
2) C
3) A
4) B
5) A
6) C
7) A
8) B
9) B
10) E
11) A
12) E
13) D
14) D
15) A
16) D
17) A
18) B
19) A
20) D
21) C
22) D
23) C
24) C
25) B
26) D
6