Skills Check

Skills Check

Question 11.1

1. In the weighted voting system ,

  1. the weight-60 voter is a dictator.
  2. the weight-60 voter has veto power.
  3. the three voters are equally powerful.

1.

b

Question 11.2

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

Question 11.3

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.

  1. The son has veto power.
  2. The daughters are dummies.
  3. The three siblings have equal voting power.

3.

c

Question 11.4

4. How many dummies are there in the voting system ?

4.

3

Question 11.5

5. The voters , , and use the voting system. In which permutation is the pivotal voter?

5.

c

Question 11.6

6. Four voters, , use the weighted voting system. In the permutation DBCA, the pivotal voter is ________.

6.

C

Question 11.7

7. If the first voter in some permutation is the pivotal voter, then

  1. that voter must be the dictator.
  2. that voter has veto power.
  3. the other voters are dummies.
  4. Answers (a), (b), and (c) are all correct.

7.

d

495

Question 11.8

8. The Shapley–Shubik index of the weight-1 voter in the voting system is ____________.

8.

, or 8.33%

Question 11.9

9. The number (7 factorial) is

  1. more than 1 million.
  2. between 10,000 and 1 million.
  3. less than 10,000.

9.

c

Question 11.10

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

Question 11.11

11. If a winning coalition is minimal, the number of extra votes is

  1. zero.
  2. less than the weight of the least powerful member of the coalition.
  3. more than the weight of the least powerful member who is opposed.

11.

b

Question 11.12

12. If a motion passes in the weighted voting system with only the weight-2 voter dissenting, then the critical voters are those with weights _____________.

12.

4 and 3

Question 11.13

13. A voting system has the following winning coalitions: , , , and . Which voter is the most powerful?

13.

b

Question 11.14

14. The minimal winning coalitions of a voting system are , , and . In the winning coalition , ____________ are the critical voters.

14.

, , and

Question 11.15

15. Referring to the voting system in Skills Check 14, which voter is not critical in the winning coalition ?

15.

a

Question 11.16

16. In the voting system described in Skills Check 14, voter has ____________ power.

16.

veto

Question 11.17

17. If voter X is critical in every winning coalition, then

  1. X has veto power.
  2. X is a dictator.
  3. X will be needed to prevent a motion from passing.
  4. Answers (a), (b), and (c) are all correct.

17.

a

Question 11.18

18. In a system with voters, is a dictator. The Banzhaf power index of is _________.

18.

Question 11.19

19. In the weighted voting system , what is the Banzhaf power index of the weight-1 voter?

  1. 2
  2. 1
  3. 0

19.

c

Question 11.20

20. Voters use the voting system . _________ is a minimal winning coalition that has 1 extra vote.

20.

Question 11.21

21.

  3. Neither (a) nor (b) is correct.

21.

b

Question 11.22

22. _________.

22.

20

Question 11.23

23.

  2. 220
  3. Answers (a) and (b) are both correct.

23.

c

Question 11.24

24. In the voting system , the Banzhaf power index of a weight-1 voter is _______________.

24.

Question 11.25

25. Four voters, , use the weighted voting system . The Banzhaf index of B is

  1. 0.
  2. 1.
  3. 2.
  4. 3.

25.

d

Question 11.26

26. The Banzhaf power index of the weight-3 voter in the system is ______________.

26.

Question 11.27

27. The weighted voting system is equivalent to

  1. .
  2. .
  3. .
  4. All of the above answers are right.

27.

d

Question 11.28

28. The minimal winning coalitions of the system , with voters named , and , are __________.

28.

, , and

Question 11.29

29. The minimal winning coalitions of a voting system are and . Which weighted voting system is equivalent to it?

  4. The system is not equivalent to a weighted voting system.

29.

a

496

Question 11.30

30. If the minimal winning coalitions are and , _____________ has veto power.

30.