Frontiers of Microeconomics 5463
Table 22-7
Suppose that residents of a town are asked to vote on the best way to improve the safety of an
intersection. The three choices are: a stoplight, a 4-way stop, and a 2-way stop. The voters are
divided into three groups based on their preferences.
Voter Type
Type 1
Type 2
Type 3
Percent of Electorate
40
40
20
1st Choice
4-way stop
stoplight
2-way stop
2nd Choice
2-way stop
4-way stop
4-way stop
3rd Choice
stoplight
2-way stop
stoplight
52. Refer to Table 22-7. If the first vote pits a stoplight against a 4-way stop and the second vote
pits a 2-way stop against the winner of the first vote, then the outcome is as follows:
a. 4–way stop wins the first vote and 4-way stop wins the second vote, so the town installs a 4-
way stop.
b. 4-way stop wins the first vote and 2-way stop wins the second vote, so the town installs a 2-
way stop.
c. Stoplight wins the first vote and stoplight wins the second vote, so the town installs a stoplight.
d. Stoplight wins the first vote and 2-way stop wins the second vote, so the town installs a 2-way
stop.
5464 Frontiers of Microeconomics
53. Refer to Table 22-7. If the first vote pits a 2-way stop against a 4-way stop and the second vote
pits a stoplight against the winner of the first vote, then the outcome is as follows:
a. 2–way stop wins the first vote and 2-way stop wins the second vote, so the town installs a 2-
way stop.
b. 2–way stop wins the first vote and stoplight wins the second vote, so the town installs a
stoplight.
c. 4–way stop wins the first vote and 4-way stop wins the second vote, so the town installs a 4-
way stop.
d. 4–way stop wins the first vote and stoplight wins the second vote, so the town installs a
stoplight.
54. Refer to Table 22-7. If the first vote pits a 2-way stop against a stoplight and the second vote
pits a 4-way stop against the winner of the first vote, then the outcome is as follows:
a. 2–way stop wins the first vote and 2-way stop wins the second vote, so the town installs a 2-
way stop.
b. 2–way stop wins the first vote and 4-way stop wins the second vote, so the town installs a 4-
way stop.
c. Stoplight wins the first vote and stoplight wins the second vote, so the town installs a stoplight.
d. Stoplight wins the first vote and 4-way stop wins the second vote, so the town installs a 4-way
stop.
Frontiers of Microeconomics 5465
55. Refer to Table 22-7. Which of the following statements is correct regarding the Condorcet
paradox and the results of pairwise voting on how to improve the safety of the intersection?
a. The paradox implies that pairwise voting never produces transitive preferences, and so the
voting in the town fails to produce transitive preferences.
b. The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive
preferences, but the voting in the town does produce transitive preferences.
c. The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive
preferences, and the voting in the town fails to produce transitive preferences.
d. The paradox implies that pairwise voting always produces transitive preferences, and so the
voting in the town produces transitive preferences.
56. Refer to Table 22–7. If the vote were conducted according to a Borda count system where
each person’s first choice receives 3 points, second choice 2 points, and third choice 1 point, the
result would be
a. a 2-way stop.
b. a 4-way stop.
c. a stoplight
d. a tie between a 2-way stop and a stoplight.
5466 Frontiers of Microeconomics
57. Refer to Table 22-7. Based on the information in the table, which of the following statements is
true?
a. In a vote between a 2-way stop and a stoplight, stoplight wins because 40% of voters have
stoplight as their 1st choice.
b. In a vote between a 2-way stop and a 4-way stop, the 4-way stop wins getting 80% of the total
vote.
c. In a vote between a 4-way stop and a stoplight, there is a tie because each gets 40% of the
vote.
d. None of the above are true.
Table 22-8
The citizens of Mayville are having a severe budget shortage and are faced with eliminating
athletics from the town high school. The town administrator has determined that the town can
afford to maintain one sport. Exactly one of the three choices will prevail, and the choice will be
made by way of pairwise voting, with the majority determining the outcome on each vote. The
preferences of the voters are summarized in the table below.
Voter Type
Type A
Type B
Percent of Electorate
20
42
First choice
Hockey
Football
Second choice
Football
Basketball
Third choice
Basketball
Hockey
Frontiers of Microeconomics 5467
58. Refer to Table 22–8. If the town administrator first asks the citizens to vote for hockey or
basketball and then asks them to choose between the winner of the first vote and football, what
will be the outcome?
a. Hockey will win the first vote and hockey will win the second vote.
b. Hockey will win the first vote and football will win the second vote.
c. Basketball will win the first vote and basketball will win the second vote.
d. Basketball will win the first vote and football will win the second vote.
59. Refer to Table 22–8. The town administrator is a huge basketball fan. If he wants to ensure that
basketball is the winning sport, how should he set up the voting?
a. First vote: hockey vs. basketball; Second vote: winner of first vote vs. football
b. First vote: hockey vs. football; Second vote: winner of first vote vs. basketball
c. First vote: basketball vs. football; Second vote: winner of first vote vs. hockey
d. It is impossible for basketball to win according to Arrow’s impossibility theorem.
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60. Refer to Table 22-8. If a Borda count is used, what will be the outcome of the voting?
a. Basketball will win.
b. Football will win.
c. Hockey will win.
d. Football and basketball will tie.
Table 22-9
Voter Type
Type 1
Type 2
Type 3
Type 4
Percent of electorate
32
20
15
33
First choice
D
C
A
B
Second choice
C
A
D
D
Third choice
B
D
B
A
Fourth choice
A
B
C
C
61. Refer to Table 22–9. The table shows the preferences of four types of voters over four possible
outcomes: A, B, C, D. In addition, the table shows the percentage of voters of each type. Based
on this information, which of the following statements is false?
a. Outcome D is preferred to outcome C overall.
b. Outcome C is preferred to outcome B overall.
c. Outcome B is preferred to outcome D overall.
d. Outcome D is preferred to outcome A overall.
Frontiers of Microeconomics 5469
62. Refer to Table 22–9. The table shows the preferences of four types of voters over four possible
outcomes: A, B, C, D. In addition, the table shows the percentage of voters of each type. Given
pairwise voting in which voters choose first between A and B, then between the winner of the
first vote and C, and finally between the winner of the second vote and D, which outcome would
win?
a. A
b. B
c. C
d. D
63. Refer to Table 22–9. The table shows the preferences of four types of voters over four possible
outcomes: A, B, C, and D. In addition, the table shows the percentage of voters of each type.
Suppose a Borda count election is held in which each voter ranks the four outcomes, giving 1
point to last place, 2 points to second to last, 3 points to the second best, and 4 points to the best.
In this case, which outcome would win?
a. A
b. B
c. C
d. D
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64. Refer to Table 22–9. The table shows the preferences of four types of voters over four possible
outcomes: A, B, C, and D. In addition, the table shows the percentage of voters of each type.
Suppose that, for some reason, D is eliminated as a possible option. Using a Borda count election,
with 3 points for the best choice, 2 points for the second best choice, and 1 point for the last
choice, which outcome would win this election?
a. A
b. B
c. C
d. There would be a three-way tie.
Frontiers of Microeconomics 5471
Table 22–10
The town of Franklin is facing a severe budget shortage. The town administrator has proposed
four options to balance the budget: increase property taxes (taxes), cut the school arts budget
(arts), turn off half of the streetlights in the town (streetlights), reduce police patrols (police).
Exactly one of the four choices will prevail, and the choice will be made by way of pairwise
voting, with the majority determining the outcome on each vote. The preferences of the voters are
summarized in the table below.
Voter Type
Type A
Type B
Type C
Type D
14
40
28
18
taxes
streetlights
arts
police
police
arts
taxes
arts
streetlights
taxes
police
streetlights
arts
police
streetlights
taxes
65. Refer to Table 22–10. If the town administrator asks voters to choose first between reducing
police patrols and increasing taxes, and then between the winner of the first vote and cutting the
school arts budget, and then between the winner of the second vote and turning off half of the
streetlights, which choice will win the final vote?
a. arts
b. police
c. streetlights
d. taxes
5472 Frontiers of Microeconomics
66. Refer to Table 22–10. If the town administrator asks voters to choose first between increasing
taxes and turning off half of the streetlights, and then between the winner of the first vote and
reducing police patrols, and then between the winner of the second vote and cutting the school
arts budget, which choice will win the final vote?
a. arts
b. police
c. streetlights
d. taxes
67. Refer to Table 22–10. If a Borda count is used, which option will win?
a. arts
b. police
c. streetlights
d. taxes
Frontiers of Microeconomics 5473
Table 22–11
Five voters must choose from among four options: A, B, C, or D. Each voter’s preferences are
summarized in the table below. Options higher in the table are more preferred by the voter.
Preferences
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5
1st Choice
D
C
B
C
A
2nd Choice
A
B
A
D
D
3rd Choice
B
A
D
B
C
4th Choice
C
D
C
A
B
68. Refer to Table 22-11. If the vote were conducted according to a Borda count system where
each person’s first choice receives 4 points, second choice 3 points, third choice 2 points and
fourth choice 1 point, the result would be
a. that A would win.
b. that B would win.
c. that C would win.
d. a tie between A and D.
69. Refer to Table 22-11. If the vote were conducted according to a modified Borda count system
where each person‘s first choice receives 10 points, second choice 5 points, third choice 3 points
and fourth choice 1 point, the result would be that
a. A would win.
b. B would win.
c. C would win.
d. D would win.
5474 Frontiers of Microeconomics
70. Refer to Table 22-11. Which pairwise voting scheme would result in outcome B?
a. First, choose between A and B. Second, voters choose between the winner of the first vote
and C. Third, voters choose between the winner of the second vote and D.
b. First, choose between B and C. Second, voters choose between the winner of the first vote and
A. Third, voters choose between the winner of the second vote and D.
c. First, choose between B and D. Second, voters choose between the winner of the first vote
and C. Third, voters choose between the winner of the second vote and A.
d. First, choose between C and D. Second, voters choose between the winner of the first vote
and A. Third, voters choose between the winner of the second vote and B.
71. Refer to Table 22-11. Which pairwise voting scheme would result in outcome D?
a. First, choose between A and B. Second, voters choose between the winner of the first vote
and C. Third, voters choose between the winner of the second vote and D.
b. First, choose between B and D. Second, voters choose between the winner of the first vote
and C. Third, voters choose between the winner of the second vote and A.
c. First, choose between C and D. Second, voters choose between the winner of the first vote
and A. Third, voters choose between the winner of the second vote and B.
d. First, choose between C and D. Second, voters choose between the winner of the first vote
and B. Third, voters choose between the winner of the second vote and A.
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72. Refer to Table 22-11. Which pairwise voting scheme would result in outcome A?
a. First, choose between A and B. Second, voters choose between the winner of the first vote
and C. Third, voters choose between the winner of the second vote and D.
b. First, choose between A and C. Second, voters choose between the winner of the first vote
and B. Third, voters choose between the winner of the second vote and D.
c. First, choose between B and D. Second, voters choose between the winner of the first vote
and C. Third, voters choose between the winner of the second vote and A.
d. First, choose between C and D. Second, voters choose between the winner of the first vote
and A. Third, voters choose between the winner of the second vote and B.
73. Refer to Table 22–11. The town administrator would much rather have more tax revenue than
have to cut any programs or services. If he wants to ensure that winning choice from voting is
increasing taxes, how should he set up the voting?
a. First vote: taxes vs. streetlights; Second vote: winner of the first vote vs. police; Third vote:
winner of the second vote vs. arts
b. First vote: arts vs. streetlights; Second vote: winner of the first vote vs. police; Third vote:
winner of the second vote vs. taxes
c. First vote: police vs. taxes; Second vote: winner of the first vote vs. arts; Third vote: winner of
the second vote vs. streetlights
d. The town administrator should use a Borda count.
5476 Frontiers of Microeconomics
Table 22–12
The following table shows the preferences for the five voters in a city regarding how to deal with
the city’s diseased trees.
Voter #
1
2
3
4
5
1st choice
B
B
C
D
A
2nd choice
C
C
D
C
C
3rd choice
D
A
A
A
D
4th choice
A
D
B
B
B
A = do nothing
B = follow the expert’s advice to remove every tree
C = remove every 4th tree now and perhaps more later D = use an untested spraying alternative
74. Refer to Table 22-12. Consider the public policy for dealing with the diseased trees. Using
pairwise majority voting with A versus B, then the winner of that vote versus C, then the winner
of that vote versus D, which policy wins?
a. A
b. B
c. C
d. D
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75. Refer to Table 22–12. Consider the public policy for dealing with the diseased trees. Using a
Borda count with 4 points assigned to the first choice, 3 points assigned to the second choice, 2
points assigned to the third choice, and 1 point assigned to the fourth choice, which policy wins?
a. A
b. B
c. C
d. D
76. Refer to Table 22–12. Consider the public policy for dealing with diseased trees. Based on the
preferences in the table, which of the following statements is correct?
a. Outcome D is preferred to outcome C overall.
b. Outcome B is preferred to outcome C overall.
c. Outcome D is preferred to outcome B overall.
d. Outcome A is preferred to outcome D overall.
5478 Frontiers of Microeconomics
Table 22–13
A high school Spanish class and their teacher are planning to take a Spring Break trip abroad but
they have to decide where to go. They have narrowed the options to: Spain, Mexico, Ecuador,
and Costa Rica. The voters’ preferences are shown in the table below.
Voter
First Choice
Second Choice
Third Choice
Fourth Choice
1
Spain
Mexico
Ecuador
Costa Rica
2
Costa Rica
Mexico
Ecuador
Spain
3
Spain
Mexico
Ecuador
Costa Rica
4
Ecuador
Costa Rica
Mexico
Spain
5
Costa Rica
Mexico
Ecuador
Spain
6
Spain
Costa Rica
Ecuador
Mexico
7
Spain
Mexico
Ecuador
Costa Rica
8
Costa Rica
Mexico
Ecuador
Spain
9
Mexico
Ecuador
Spain
Costa Rica
10
Spain
Mexico
Ecuador
Costa Rica
11
Spain
Mexico
Ecuador
Costa Rica
12
Ecuador
Mexico
Costa Rica
Spain
13
Costa Rica
Mexico
Ecuador
Spain
14
Costa Rica
Ecuador
Mexico
Spain
15
Mexico
Spain
Costa Rica
Ecuador
16
Ecuador
Costa Rica
Spain
Mexico
17
Mexico
Spain
Ecuador
Costa Rica
18
Costa Rica
Ecuador
Mexico
Spain
19
Spain
Mexico
Costa Rica
Ecuador
20
Mexico
Ecuador
Spain
Costa Rica
21
Costa Rica
Ecuador
Mexico
Spain
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77. Refer to Table 22–13. In a pairwise election between Costa Rica and Ecuador and then a
second election between the winner and Mexico, which countries are chosen?
a. Costa Rica is chosen in the in the first and second elections.
b. Costa Rica is chosen in the first election and Mexico is chosen in the second.
c. Ecuador is chosen in the first and second elections.
d. Ecuador is chosen in the first election and Mexico is chosen in the second.
78. Refer to Table 22–13. In a pairwise election between Mexico and Ecuador and then a second
election between the winner and Costa Rica, which countries are chosen?
a. Ecuador is chosen in the in the first and second elections.
b. Ecuador is chosen in the first election and Costa Rica is chosen in the second.
c. Mexico is chosen in the first and second elections.
d. Mexico is chosen in the first election and Costa Rica is chosen in the second.
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79. Refer to Table 22–13. In a pairwise election between Mexico and Spain and then a second
election between the winner and Costa Rica, which countries are chosen?
a. Mexico is chosen in the first and second elections.
b. Mexico is chosen in the first election and Costa Rica is chosen in the second.
c. Spain is chosen in the first and second elections.
d. Spain is chosen in the first election and Costa Rica is chosen in the second.
80. Economist Kenneth Arrow wrote a famous book in 1951 in which he took up the question,
a. Is there a perfect voting system?
b. Are preferences transitive?
c. Is a dictatorship a good form of government?
d. Does Democracy work?
Frontiers of Microeconomics 5481
81. In his 1951 book, Social Choice and Individual Values, Kenneth Arrow defined a “perfect”
voting system. That system includes which of the following features?
a. unanimity
b. transitivity
c. absence of a dictator
d. All of the above are correct.
82. In his 1951 book, Social Choice and Individual Values, Kenneth Arrow used the term
“unanimity” to mean
a. A beats B only if everyone prefers A to B.
b. if everyone prefers A to B, then A beats B.
c. if A beats B and B beats C, then A must best C.
d. everyone who is eligible to vote must vote; otherwise, the outcome is invalid.
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83. In his 1951 book, Social Choice and Individual Values, Kenneth Arrow used the term
“transitivity” to mean
a. A beats B only if everyone prefers A to B.
b. if everyone prefers A to B, then A beats B.
c. if A beats B and B beats C, then A must beat C.
d. everyone who is eligible to vote must vote; otherwise, the outcome is invalid.
84. In his 1951 book Social Choice and Individual Values, Arrow’s perfect voting system satisfies
all of the following properties except
a. unanimity.
b. transitivity.
c. reflexivity.
d. independence of irrelevant alternatives.