Skills Check
1. In the weighted voting system [65:60, 30, 10],
1.
b
2. A voting system has 200 voters, and a simple majority is needed to pass a motion. The quota for this system is _________.
2.
101
3. Two daughters and a son administer a trust fund. Each daughter has 4 votes, and the son has 7 votes; the quota for passing a measure is 8.
3.
c
4. How many dummies are there in the voting system [16:8, 8, 4, 2, 1]?
4.
3
5. The voters A, B, and C use the voting system[3:2, 1, 1]. In which permutation is C the pivotal voter?
5.
c
6. Four voters, A, B, C, D, use the weighted voting system[6:4, 3, 2, 1]. In the permutation DBCA, the pivotal voter is ________.
6.
C
7. If the first voter in some permutation is the pivotal voter, then
7.
d
8. The Shapley–Shubik index of the weight-1 voter in the voting system[6:4, 3, 2, 1] is ____________.
8.
112, or 8.33%
9. The number 7! (7 factorial) is
9.
c
10. A jury’s decision in a criminal trial must be unanimous. In any permutation of the jury’s members, the member who is pivotal is ____________.
10.
the last juror
11. If a winning coalition is minimal, the number of extra votes is
11.
b
12. If a motion passes in the weighted voting system [6:4, 3, 2, 1] with only the weight-2 voter dissenting, then the critical voters are those with weights _____________.
12.
4 and 3
13. A voting system has the following winning coalitions: {A,B,C}, {A,B,D}, {B,C,D}, and {A,B,C,D}. Which voter is the most powerful?
13.
b
14. The minimal winning coalitions of a voting system are {A,B,C}, {C,D,E}, and {B,C,D}. In the winning coalition {A,B,C,E}, ____________ are the critical voters.
14.
A, B, and C
15. Referring to the voting system in Skills Check 14, which voter is not critical in the winning coalition {A,C,D,E}?
15.
a
16. In the voting system described in Skills Check 14, voter C has ____________ power.
16.
veto
17. If voter X is critical in every winning coalition, then
17.
a
18. In a system with n voters, A is a dictator. The Banzhaf power index of A is _________.
18.
2n−1
19. In the weighted voting system [5:3, 2, 1], what is the Banzhaf power index of the weight-1 voter?
19.
c
20. Voters A,B,C,…,K use the voting system [19:8, 7, 6, 5, 4, 1, 1, 1, 1, 1, 1]. _________ is a minimal winning coalition that has 1 extra vote.
20.
{A,B,D}
21. 15C7+ 15C8=
21.
b
22. 6C3= _________.
22.
20
23. 12C3=
23.
c
24. In the voting system [6:4, 1, 1, 1, 1, 1], the Banzhaf power index of a weight-1 voter is _______________.
24.
4C1=4
25. Four voters, A,B,C,D, use the weighted voting system [6:4, 3, 2, 1]. The Banzhaf index of B is
25.
d
26. The Banzhaf power index of the weight-3 voter in the system [7:3, 2, 2, 2] is ______________.
26.
3C2+ 3C3=4
27. The weighted voting system [6:4, 3, 2, 1] is equivalent to
27.
d
28. The minimal winning coalitions of the system [7:3, 2, 2, 2], with voters named A,B,C, and D, are __________.
28.
{A,B,C}, {A,B,D}, and {A,C,D}
29. The minimal winning coalitions of a voting system are {A,B,C} and {B,C,D}. Which weighted voting system is equivalent to it?
29.
a
30. If the minimal winning coalitions are {A,B} and {B,C,D}, _____________ has veto power.
30.
B