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Skills Check

Skills Check

1. A preference list ballot

Question 9.1

  1. indicates only a voter’s top choice.
  2. is a rank ordering of the candidates, with no ties.
  3. will often have ties.

Question 9.2

2. To say that a voting system treats all voters equally means that _________.

2.

if any two voters exchange ballots, the election outcome is unchanged

Question 9.3

3. To say that a voting system for two candidates treats both candidates equally means that

  1. each wins if he or she receives all the votes.
  2. if all voters reverse their ballots, the election outcome changes.
  3. if any two voters exchange ballots, the election outcome is unchanged.

3.

b

Question 9.4

4. A two-candidate voting system is monotone if _______.

4.

a switch in a ballot from being a vote for the loser to being a vote for the winner doesn't change the election outcome

Question 9.5

5. May’s theorem says that, with an odd number of voters, among all two-candidate voting systems that never result in a tie, majority rule is the only one that

  1. treats both candidates equally.
  2. treats both candidates equally and all voters equally.
  3. treats both candidates equally and all voters equally and is monotone.

5.

c

Question 9.6

6. When a choice is being made between two candidates, the first type of voting system to suggest itself is __________.

6.

majority rule

Question 9.7

7. In this chapter, the “number of voters assumption” refers to the assumption that

  1. there is more than one voter.
  2. the number of voters is odd.
  3. the number of voters is even.

7.

b

Question 9.8

8. The winner with Condorcet’s method is the candidate who _____________.

8.

defeats every other candidate in a one-on-one contest

Question 9.9

9. Which of the following does not satisfy exactly two of the conditions in May’s theorem?

  1. A dictatorship
  2. Imposed rule
  3. Minority rule
  4. None of the above

9.

d

Question 9.10

10. The Hare system fails to satisfy _________.

10.

monotonicity

Question 9.11

11. Suppose Condorcet’s method is being used in an election in which Candidate A is ranked first on more than half of the ballots. Then Candidate A is

  1. the unique winner.
  2. among the winners, but there may be others.
  3. not necessarily among the winners.
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11.

a

Question 9.12

12. The flaw in Condorcet’s method is that it _________.

12.

sometimes produces no winner at all

Question 9.13

13. Condorcet’s voting paradox refers to the fact that

  1. people vote even though an individual vote virtually never affects the outcome of an election.
  2. the statement “This statement is false” can be neither true nor false.
  3. there are elections in which there is no winner using Condorcet’s method.

13.

c

Question 9.14

14. With plurality voting, the winner is the candidate who ___________.

14.

receives the most first-place votes

Question 9.15

15. George W. Bush’s defeat of Al Gore in the state of Florida in the 2000 presidential election shows that

  1. plurality voting does not satisfy the CWC.
  2. majority rule is not monotone.
  3. the Borda count does not satisfy IIA.

15.

a

Question 9.16

16. With the Borda count, the election winner is the candidate who ___________.

16.

has the highest Borda score

Question 9.17

17. Rather than assigning points and doing arithmetic, the Borda score of a candidate can be found by

  1. scanning the ballots and counting the number of occurrences of other candidates below that one.
  2. counting the number of first-place votes and multiplying by 4.
  3. counting the number of candidates that it defeats one on one.

17.

a

Question 9.18

18. Independence of irrelevant alternatives says that a nonwinner can never switch to being a winner unless at least one voter changes his or her ballot in a way that ___________.

18.

reverses the order in which this nonwinner and the winner were ranked

Question 9.19

19. The Borda count fails to satisfy

  1. monotonicity.
  2. the Pareto condition.
  3. IIA.

19.

c

Question 9.20

20. The term single transferrable vote system is sometimes used to refer to the voting system in this chapter called __________.

20.

the Hare system

Question 9.21

21. A voting system satisfies the CWC provided that, in every election,

  1. there is a Condorcet winner and this candidate is the winner of the election.
  2. if there is a Condorcet winner, then this candidate is among the winners of the election.
  3. if there is a Condorcet winner, then this candidate is the unique winner of the election.

21.

c

Question 9.22

22. Sequential pairwise voting is the voting system in which _______________.

22.

one-on-one contests take place according to an ordering of the candidates called an “agenda”

Question 9.23

23. Sequential pairwise voting fails to satisfy

  1. monotonicity.
  2. the Pareto condition.
  3. the CWC.

23.

b

Question 9.24

24. The voting system in which a voter can vote for as many candidates as he or she wishes to vote for is called ___________.

24.

approval voting

Question 9.25

25. Suppose the Borda count is being used in an election in which Candidate A is ranked first on more than half of the ballots. Then Candidate A is

  1. the unique winner.
  2. among the winners, but there may be others.
  3. not necessarily among the winners.

25.

c

Question 9.26

26. A voting system is manipulable if there are elections in which __________________________________________________________________.

26.

it is to a voter's advantage to submit a ballet that misrepresents his or her preferences

Question 9.27

27. Suppose the Hare system is being used in an election in which Candidate A is ranked first on more than half of the ballots. Then Candidate A is

  1. the unique winner.
  2. among the winners, but there may be others.
  3. not necessarily among the winners.

27.

a

Question 9.28

28. Both the Hare system and the plurality runoff method are defective in that ___________.

28.

they fail to satisfy monotonicity

Question 9.29

29. Arrow’s impossibility theorem says that with three or more candidates and any number of voters, there is no voting system that

  1. is not a dictatorship.
  2. satisfies IIA and is not a dictatorship.
  3. satisfies the Pareto condition and IIA, and is not a dictatorship.
  4. always produces a winner, satisfies the Pareto condition and IIA, and is not a dictatorship.

29.

d

Question 9.30

30. The weak version of Arrow’s impossibility theorem asserts that, with three or more candidates and an odd number of voters, there is no voting system that ___________.

30.

satisfies the Condorcet winner criterion and independence of irrelevant alternatives, and always produces at least one winner in every election.

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