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?
Outcome D is preferred to outcome C overall.
Outcome C is preferred to outcome B overall.
Outcome B is preferred to outcome D overall.
Outcome D is preferred to outcome A overall.
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
B
C
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
B
C
D
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
B
C
There would be a three-way tie.
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
% of Electorate
14
40
28
18
First choice
taxes
streetlights
arts
police
Second choice
police
arts
taxes
arts
Third choice
streetlights
taxes
police
streetlights
Fourth choice
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?
arts
police
streetlights
taxes
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?
arts
police
streetlights
taxes
67. Refer to Table 22–10. If a Borda count is used, which option will win?
arts
police
streetlights
taxes
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
that A would win.
that B would win.
that C would win.
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 would win.
B would win.
C would win.
D would win.
70. Refer to Table 22–11. Which pairwise voting scheme would result in outcome B?
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.
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.
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.
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?
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.
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.
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.
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.
72. Refer to Table 22–11. Which pairwise voting scheme would result in outcome 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.
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.
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.
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?
First vote: taxes vs. streetlights; Second vote: winner of the first vote vs. police; Third vote: winner of the
second vote vs. arts
First vote: arts vs. streetlights; Second vote: winner of the first vote vs. police; Third vote: winner of the
second vote vs. taxes
First vote: police vs. taxes; Second vote: winner of the first vote vs. arts; Third vote: winner of the second vote
vs. streetlights
The town administrator should use a Borda count.
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
B
C
D
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
B
C
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?
Outcome D is preferred to outcome C overall.
Outcome B is preferred to outcome C overall.
Outcome D is preferred to outcome B overall.
Outcome A is preferred to outcome D overall.
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
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?
Costa Rica is chosen in the in the first and second elections.
Costa Rica is chosen in the first election and Mexico is chosen in the second.
Ecuador is chosen in the first and second elections.
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?
Ecuador is chosen in the in the first and second elections.
Ecuador is chosen in the first election and Costa Rica is chosen in the second.
Mexico is chosen in the first and second elections.
Mexico is chosen in the first election and Costa Rica is chosen in the second.
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?
Mexico is chosen in the first and second elections.
Mexico is chosen in the first election and Costa Rica is chosen in the second.
Spain is chosen in the first and second elections.
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,
Is there a perfect voting system?
Are preferences transitive?
Is a dictatorship a good form of government?
Does Democracy work?
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?
unanimity
transitivity
absence of a dictator
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 beats B only if everyone prefers A to B.
if everyone prefers A to B, then A beats B.
if A beats B and B beats C, then A must best C.
everyone who is eligible to vote must vote; otherwise, the outcome is invalid.
83. In his 1951 book, Social Choice and Individual Values, Kenneth Arrow used the term “transitivity” to mean
A beats B only if everyone prefers A to B.
if everyone prefers A to B, then A beats B.
if A beats B and B beats C, then A must beat C.
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
unanimity.
transitivity.
reflexivity.
independence of irrelevant alternatives.
85. Arrow’s impossibility theorem shows that no voting system can satisfy which of the following properties?
unanimity and transitivity only
transitivity and independence of irrelevant alternatives only
no dictators and transitivity only
unanimity, transitivity, independence of irrelevant alternatives, and no dictators
86. One property of Kenneth Arrow’s “perfect” voting system is that the ranking between any two outcomes A and B
should not depend on whether some third outcome C is also available. Arrow called this property
transitivity.
pairwise perfection.
independence of irrelevant alternatives.
irrelevance of social choices.
87. Kenneth Arrow proved that the voting system that satisfied all of the properties of his “perfect” voting system was
one in which a single person (a “dictator”) imposes his preferences on everyone else.
pairwise majority voting.
majority voting that is not pairwise.
None of the above is correct. Arrow proved that no voting system can satisfy all of the properties of his
“perfect” system.
88. The Borda count fails to satisfy which of Kenneth Arrow’s properties of a “perfect” voting system?
no dictator
unanimity
transitivity
independence of irrelevant alternatives
89. The Arrow impossibility theorem shows that
democracy should be abandoned as a form of government.
it is impossible to improve upon democratic voting methods as a mechanism for social choice.
all voting systems are flawed as a mechanism for social choice.
the median voter’s preferences will always win in a two-way vote.
90. Arrow’s impossibility theorem is “disturbing” in the sense that it proves that
no voting system is perfect.
only a dictator can produce a desirable social outcome.
the preferences of the wealthy should be given more weight than the preferences of the poor.
the centuries-old Condorcet paradox was not a paradox after all.
91. What is the name of the mathematical result showing that no voting system can simultaneously satisfy the properties
of unanimity, transitivity, independence of irrelevant alternatives, and no dictators?
The fundamental theorem of behavioral economics
Arrow’s impossibility theorem
The fundamental theorem of voting
The median voter theorem
92. Suppose the voters in a small country are choosing between two options, A and B. After the voting is complete it is
discovered that option A received 100% of the votes with option B receiving no votes. After the vote, however, the
country’s leader decides that option B is better for the people and implements B rather than A. The voting system in this
country fails which of Arrow’s properties of a desirable voting system?
unanimity
transitivity
independence of irrelevant alternatives
No dictators
93. In a vote between options A, B, and C, option C wins. When option B is eliminated and a vote is taken between option
A and option C, option A wins. The voting system used fails to satisfy which of Arrow’s properties of a desirable voting
system?
unanimity
transitivity
independence of irrelevant alternatives
No dictators
94. Suppose that in a Borda count election, outcome X is preferred to outcome Y, and outcome Y is preferred to outcome
Z, when outcomes X, Y, and Z are all available options. When Y is removed as an option, however, outcome Z is
preferred to outcome X. This would violate Arrow’s assumption that voting systems should satisfy
unanimity.
transitivity.
the independence of irrelevant alternatives.
no dictators.
Table 22–14
Amy, Beth, and Connie are on a hiring committee. They have interviewed 3 candidates identified by their last names and
are going to vote on which one is hired.
Amy
Beth
Connie
First choice
Adams
Brown
Adams
Second choice
Brown
Campbell
Campbell
Third choice
Campbell
Adams
Brown
‘
95. Refer to Table 22–14. Below are lists of results for two separate elections between two candidates. In which case are
both results correct?
Adams wins over Brown and Brown wins over Campbell
Adams wins over Brown and Campbell wins over Brown
Brown wins over Adams and Brown wins over Campbell
Brown wins over Adams and Campbell wins over Brown
96. Refer to Table 22–14. Which results for pairwise voting are correct?
In a vote between Adams and Campbell, and then a vote between the winner and Brown, Adams wins.
In a vote between Brown and Campbell, and then a vote between the winner and Adams, Adams wins.
Both A and B are correct.
Neither A nor B is correct.
97. Refer to Table 22–14. Which of the following is correct for this election? There is
both transitivity and independence of irrelevant alternatives.
transitivity but not independence of irrelevant alternatives.
independence of irrelevant alternatives. but not transitivity.
neither transitivity nor independence of irrelevant alternatives.
98. Refer to Table 22–14. What would the results of a Borda Count vote be?
Adams and Brown tie.
Adams wins.
Brown wins.
Campbell wins.
99. Refer to Table 22–14. Adams calls and says she’s accepted another position. In which case does Campbell win
against Brown?
both a pairwise vote and a Borda Count vote
a pairwise vote, but not a Borda Count vote
a Borda Count vote, but not a pairwise vote
neither a Borda Count vote, nor a pairwise vote
Table 22–15
Diane, Henry, and Linda are voting for who to promote. They can only promote one candidate. Their preferences are
given in the table below.
Diane
Henry
Linda
1st Choice
Beth
Fred
Mary
2nd Choice
Fred
Beth
Beth
3rd Choice
Mary
Mary
Fred
100. Refer to Table 22–15. If elections were held where voters choose either Fred or Beth, and then choose either the
winner or Mary, what would the results be?
Fred would win the first and second election.
Fred would win the first election and Mary would win the second.
Beth would wind the first and second election.
Beth would win the first election and Mary would win the second.
101. Refer to Table 22–15. If elections were held where voters choose either Fred or Mary, and then choose either the
winner or Beth, what would the results be?
Fred would win the first and second elections.
Fred would win the first election and Beth would win the second election.
Mary would win the first and second elections.
Mary would win the first election and Beth would win the second election.
102. Refer to Table 22–15. If elections were held where voters choose either Beth or Mary, and then choose either the
winner or Fred, what would the results be?
Beth would win both elections.
Beth would win the first election and Fred would win the second election.
Mary would win the first and second elections.
Mary would win the first election and Fred would win the second election.
103. Refer to Table 22–15. Which of the following statements is correct regarding the Condorcet paradox and the results
of pairwise voting by Henry, Diane, and Linda?
The paradox implies that pairwise voting never produces transitive preferences, and so the voting by Henry,
Diane, and Linda fails to produce transitive preferences.
The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences, and the
voting by Henry, Diane, and Linda does produce transitive preferences.
The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences,
and the voting by Henry, Diane, and Linda fails to produce transitive preferences.
The paradox does not apply to the case at hand, because Henry’s preferences are not individually transitive.
104. Refer to Table 22–15. 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,
Beth would win.
Fred would win.
Mary would win.
Fred and Mary would tie.
Table 22–16
The Johnson family is planning a vacation and, though Mr. and Mrs. Johnson will be paying for the trip, they have
decided to use a democratic voting process to choose their destination. The family members’ preferences are reflected in
the table below.
Mr. Jack
Johnson
Mrs. Jill
Johnson
Janie
Julie
Justin
1st choice
Grand Canyon
Opryland
Opryland
Disneyland
Sea World
2nd choice
Sea World
Grand Canyon
Disneyland
Grand Canyon
Disneyland
3rd choice
Opryland
Disneyland
Grand Canyon
Sea World
Grand Canyon
4th choice
Disneyland
Sea World
Sea World
Opryland
Opryland
105. Refer to Table 22-16. Mr. Johnson recommends using a vote by majority rule and proposes first choosing between
Opryland and the Grand Canyon, then choosing between the winner of the first vote and Sea World, and finally choosing
between the winner of the second vote and Disneyland. If everyone votes according to their preferences,
the winner of the first vote will be Opryland, the winner of the second vote will be Sea World, and the winner
of the final vote will be Disneyland.
the winner of the first vote will be Grand Canyon, the winner of the second vote will be Grand Canyon, and
the winner of the final vote will be Disneyland.
the winner of the first vote will be Grand Canyon, the winner of the second vote will be Sea World, and the
winner of the final vote will be Disneyland.
the winner of the first vote will be Grand Canyon, the winner of the second vote will be Grand Canyon, and
the winner of the final vote will be Grand Canyon.
106. Refer to Table 22-16. Suppose that before the family can arrive at their decision, Opryland announced that it will be
closed for the season due to flooding. Mr. Johnson recommends using a vote by majority rule and proposes first choosing
between the Grand Canyon and Sea World, and then choosing between the winner of the first vote and Disneyland. If
everyone votes according to their preferences,
the winner of the first vote will be Sea World, the winner of the second vote will be Disneyland.
the winner of the first vote will be Sea World, the winner of the second vote will be Grand Canyon.
the winner of the first vote will be Grand Canyon, the winner of the second vote will be Disneyland.
the winner of the first vote will be Grand Canyon, the winner of the second vote will be Grand Canyon.
107. Refer to Table 22-16. Mr. Johnson recommends using a vote by majority rule. If he wants to ensure that his 1st
choice becomes the family’s winning destination, he should propose
first choosing between Opryland and the Grand Canyon, then choosing between the winner of the first vote
and Sea World, and finally choosing between the winner of the second vote and Disneyland.
first choosing between Disneyland and Sea World, then choosing between the winner of the first vote and the
Grand Canyon and finally choosing between the winner of the second vote and the Opryland.
first choosing between Sea World and the Grand Canyon, then choosing between the winner of the first vote
and Disneyland, and finally choosing between the winner of the second vote and Opryland.
first choosing between Opryland and Disneyland, then choosing between the winner of the first vote and the
Grand Canyon, and finally choosing between the winner of the second vote and Sea World.
108. Refer to Table 22-16. If Mr. Johnson wants to ensure that his 1st choice becomes the family’s winning destination,
he should propose
using a vote by majority rule and first choosing between Opryland and the Grand Canyon, then choosing
between the winner of the first vote and Sea World, and finally choosing between the winner of the second
vote and Disneyland.
using a vote by majority rule and first choosing between Disneyland and Sea World, then choosing between
the winner of the first vote and the Grand Canyon and finally choosing between the winner of the second vote
and the Opryland.
using a vote by majority rule and first choosing between Sea World and the Grand Canyon, then choosing
between the winner of the first vote and Disneyland, and finally choosing between the winner of the second
vote and Opryland.
using a Borda count.
109. Refer to Table 22-16. If the family uses a Borda count to make their decision, what is their vacation destination?
Grand Canyon
Sea World
Opryland
Disneyland
110. Refer to Table 22-16. Suppose that before the family can arrive at their decision, Opryland announced that it will be
closed for the season due to flooding. If the family uses a Borda count, their vacation destination will be
Grand Canyon
Sea World
Disneyland
There is a tie between the Grand Canyon and Disneyland.
111. Majority rule will produce the outcome most preferred by the median voter, as demonstrated by the
Arrow impossibility theorem.
Condorcet paradox.
pairwise voting proposition.
median voter theorem.
112. When each voter has a most-preferred outcome for the expenditure on a particular government program, majority
rule will produce the outcome
preferred by the mean (average) voter.
preferred by the median voter.
that causes the political party in power to increase its power.
defined by Arrow’s Impossibility Theorem.