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85. Arrow’s impossibility theorem shows that no voting system can satisfy which of the following
properties?
a. unanimity and transitivity only
b. transitivity and independence of irrelevant alternatives only
c. no dictators and transitivity only
d. 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
a. transitivity.
b. pairwise perfection.
c. independence of irrelevant alternatives.
d. irrelevance of social choices.
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87. Kenneth Arrow proved that the voting system that satisfied all of the properties of his “perfect”
voting system was
a. one in which a single person (a “dictator“) imposes his preferences on everyone else.
b. pairwise majority voting.
c. majority voting that is not pairwise.
d. 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?
a. no dictator
b. unanimity
c. transitivity
d. independence of irrelevant alternatives
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89. The Arrow impossibility theorem shows that
a. democracy should be abandoned as a form of government.
b. it is impossible to improve upon democratic voting methods as a mechanism for social choice.
c. all voting systems are flawed as a mechanism for social choice.
d. 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
a. no voting system is perfect.
b. only a dictator can produce a desirable social outcome.
c. the preferences of the wealthy should be given more weight than the preferences of the poor.
d. the centuries-old Condorcet paradox was not a paradox after all.
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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?
a. The fundamental theorem of behavioral economics
b. Arrow‘s impossibility theorem
c. The fundamental theorem of voting
d. 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?
a. unanimity
b. transitivity
c. independence of irrelevant alternatives
d. No dictators
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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?
a. unanimity
b. transitivity
c. independence of irrelevant alternatives
d. 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
a. unanimity.
b. transitivity.
c. the independence of irrelevant alternatives.
d. no dictators.
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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?
a. Adams wins over Brown and Brown wins over Campbell
b. Adams wins over Brown and Campbell wins over Brown
c. Brown wins over Adams and Brown wins over Campbell
d. Brown wins over Adams and Campbell wins over Brown
96. Refer to Table 22–14. Which results for pairwise voting are correct?
a. In a vote between Adams and Campbell, and then a vote between the winner and Brown,
Adams wins.
b. In a vote between Brown and Campbell, and then a vote between the winner and Adams,
Adams wins.
c. Both A and B are correct.
d. Neither A nor B is correct.
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97. Refer to Table 22–14. Which of the following is correct for this election? There is
a. both transitivity and independence of irrelevant alternatives.
b. transitivity but not independence of irrelevant alternatives.
c. independence of irrelevant alternatives. but not transitivity.
d. neither transitivity nor independence of irrelevant alternatives.
98. Refer to Table 22-14. What would the results of a Borda Count vote be?
a. Adams and Brown tie.
b. Adams wins.
c. Brown wins.
d. Campbell wins.
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99. Refer to Table 22-14. Adams calls and says she’s accepted another position. In which case
does Campbell win against Brown?
a. both a pairwise vote and a Borda Count vote
b. a pairwise vote, but not a Borda Count vote
c. a Borda Count vote, but not a pairwise vote
d. 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?
a. Fred would win the first and second election.
b. Fred would win the first election and Mary would win the second.
c. Beth would wind the first and second election.
d. Beth would win the first election and Mary would win the second.
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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?
a. Fred would win the first and second elections.
b. Fred would win the first election and Beth would win the second election.
c. Mary would win the first and second elections.
d. 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?
a. Beth would win both elections.
b. Beth would win the first election and Fred would win the second election.
c. Mary would win the first and second elections.
d. Mary would win the first election and Fred would win the second election.
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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?
a. The paradox implies that pairwise voting never produces transitive preferences, and so the
voting by Henry, Diane, and Linda fails to produce transitive preferences.
b. 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.
c. 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.
d. 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,
a. Beth would win.
b. Fred would win.
c. Mary would win.
d. Fred and Mary would tie.
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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,
a. 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.
b. 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.
c. 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.
d. 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.
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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,
a. the winner of the first vote will be Sea World, the winner of the second vote will be
Disneyland.
b. the winner of the first vote will be Sea World, the winner of the second vote will be Grand
Canyon.
c. the winner of the first vote will be Grand Canyon, the winner of the second vote will be
Disneyland.
d. 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
a. 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.
b. 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.
c. 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.
d. 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.
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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
a. 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.
b. 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.
c. 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.
d. 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?
a. Grand Canyon
b. Sea World
c. Opryland
d. Disneyland
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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
a. Grand Canyon
b. Sea World
c. Disneyland
d. 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
a. Arrow impossibility theorem.
b. Condorcet paradox.
c. pairwise voting proposition.
d. median voter theorem.
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112. When each voter has a most-preferred outcome for the expenditure on a particular government
program, majority rule will produce the outcome
a. preferred by the mean (average) voter.
b. preferred by the median voter.
c. that causes the political party in power to increase its power.
d. defined by Arrow’s Impossibility Theorem.
113. Which voter is the voter whose views on a policy issue are in the middle of the spectrum, with
half of the voters on one side of this voter’s view and half on the other side.
a. Average voter
b. Mean voter
c. Modal voter
d. Median voter
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114. The median voter’s preferred outcome is the same as the
a. average preferred outcome.
b. outcome preferred by the greatest number of voters.
c. outcome produced by majority rule.
d. outcome preferred by Arrow’s “perfect” voter.
115. If the median voter theorem holds,
a. a Borda count will violate the principle of transitivity.
b. the Condorcet paradox also holds.
c. minority views will not receive much consideration.
d. All of the above are correct.
116. The assertion that the median voter is “king” refers directly to the result established by the
a. Arrow impossibility theorem.
b. Condorcet paradox.
c. median voter theorem.
d. Borda mechanism.
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117. The median voter
a. is the voter exactly in the middle of the distribution.
b. is the voter whose preferred outcome beats any other proposal in a two-way race.
c. always has more than half the votes on his side in a two-way race.
d. All of the above are correct.
118. According to the median voter theorem, majority rule will
a. always produce an inconclusive outcome.
b. produce the outcome least preferred by the median voter.
c. produce the outcome most preferred by the median voter.
d. produce an outcome that is inconsistent with transitive preferences.
119. The median-voter theorem explains why
a. politicians take extreme stands on issues.
b. voters are attracted to political outsiders.
c. two opposing politicians tend to take opposite sides of each issues.
d. politicians tend to take middle–of–the-road positions.
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120. When Republicans and Democrats offer similar platforms in an election campaign, a likely
explanation is the
a. Arrow impossibility theorem.
b. Condorcet paradox.
c. median voter theorem.
d. fact that politicians are more interested in the national interest than their own self-interest.
121. An implication of the median voter theorem is that, in a race between Republicans and
Democrats,
a. if Republicans want to win, they will take a “middleoftheroad” stance on many issues.
b. if Democrats want to win, they will take an extreme stance on many issues.
c. Republicans and Democrats go to extremes to differentiate themselves from one another.
d. Republicans and Democrats work hard to identify the fringe voters.
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122. In American politics, we often observe that during a campaign, the Democratic and Republican
positions on many issues are similar, which illustrates
a. Arrow’s impossibility theorem.
b. the Condorcet paradox.
c. a Borda count.
d. the median voter theorem.
123. An implication of the median voter theorem is that
a. minority views and majority views are given equal weight.
b. platforms of the major political parties will not differ greatly.
c. the logic of democracy is fundamentally flawed.
d. behavioral economics plays a significant role in voting outcomes.
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124. Assume there are nine voters in a certain small town and let x = the preferred number of dollars
spent per person per month on garbage collection. For Voters 1, 2 3, and 4, x = $10; for Voter 5,
x = $15; for Voter , x = $18; and for Voters 6, 7, 8 and 9, x = $20. The median voter is
a. Voter 3.
b. Voter 4.
c. Voter 5.
d. Voter 6.
125. Assume there are nine voters in a certain small town and let x = the preferred number of dollars
spent per person per month on garbage collection. For Voters 1, 2, and 3, x = $10; for Voter 4, x
= $15; for Voter 5, x = $18; and for Voters 6, 7, 8 and 9, x = $20. Based on these preferences,
which of these dollar amounts will win over any one of the others?
a. $10.
b. $15.
c. $18
d. $20.