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Frontiers of Microeconomics 5503
126. Assume there are 4065 voters in a certain small town and let x = the preferred number of dollars
charged monthly to support local parks. For Voters 1-1050, x = $10; for voters 1051-2121, x=
$20, for voters 2122-3334, x = $30; for voters 3335-3998, x = $40; and for 3999-4065, x = $50.
Based on these preferences, which of the dollar amounts will win over any of the others?
a. $20.
b. $30.
c. $50.
d. None of the above are correct.
127. A community has five voters who are interested in only one issue: the government’s spending on
local parks. If Andre would like the government to spend $12,000 on parks, Brandon prefers
$7,000, Charlene prefers $4,000, Dennis prefers $2,000, and Ernie prefers $0, how much
spending would a politician seeking to win the election select when running against one
opponent?
a. $2,000
b. $4,000
c. $7,000
d. $12,000
5504 Frontiers of Microeconomics
128. Suppose that there are 175 voters in an election and that 80 of them prefer a $100 budget while
the remainder prefer a $150 budget. Which of the following statements is true?
a. The Condorcet Paradox predicts that the $100 budget will win even though fewer people
prefer that budget.
b. The median voter theorem predicts that the winning budget will be $125, the median of the
preferences of the two types of voters.
c. Arrow's impossibility theorem says that the winning budget cannot be determined in this
election since there is no unanimity.
d. None of the above.
Scenario 22-3
At issue in a particular city vote is how much to spend, per person, on road repair next year.
Among the 10,000 voters, 2,900 prefer to spend $500 per person, but no more; 2,200 prefer to
spend $600 per person, but no more; 1,900 prefer to spend $800 per person, but no more; 1,600
prefer to spend $1,200 but no more, and 1,400 prefer to spend $1,400 per person, but no more.
129. Refer to Scenario 22-3. The median voter is one who prefers to spend
a. $500.
b. $600.
c. $800.
d. None of the above are correct.
Frontiers of Microeconomics 5505
130. Refer to Scenario 22-3. If there is a vote on whether to spend $600 per person or $800 per
person, the median voter will vote to spend
a. $800 per person and the voting outcome will be $800 per person.
b. $800 per person and the voting outcome will be $600 per person.
c. $600 per person and the voting outcome will be $800 per person.
d. $600 per person and the voting outcome will be $600 per person.
131. Refer to Scenario 22-3. If there is a vote on whether to spend $800 per person or $1,200 per
person, the median voter will vote to spend
a. $800 per person and the voting outcome will be $800 per person.
b. $800 per person and the voting outcome will be $1200 per person.
c. $1200 per person and the voting outcome will be $800 per person.
d. $1200 per person and the voting outcome will be $1200 per person.
5506 Frontiers of Microeconomics
Table 22-17
Voter Type
Type 1
Type 2
Type 3
Percent of electorate
55
30
15
First choice
C
B
A
Second choice
B
A
B
Third choice
A
C
C
132. Refer to Table 22-17. The table shows the preferences of three types of voters over three
possible outcomes: A, B, and C. In addition, the table shows the percentage of voters of each
type. Based on this information, which of the following statements is true?
a. As the Condorcet Paradox predicts, majority rule fails to produce transitive preferences for
society.
b. As Arrow's Impossibility Theorem demonstrates, it is impossible from this information to
determine which outcome the voters prefer.
c. The median voter theorem allows us to conclude that in a vote between B and C, B will win
since the Type 2 voter is the median voter.
d. While the Condorcet Paradox predicts that majority rule may not produce transitive
preferences for society as a whole, society's preferences in this case are transitive.
Frontiers of Microeconomics 5507
133. Refer to Table 22-17. The table shows the preferences of three types of voters over three
possible outcomes: A, B, and C. The table also shows the percentage of voters of each type.
Based on this information, which voter type is the median voter?
a. Type 1
b. Type 2
c. Type 3
d. The median voter cannot be determined without knowing the pair of outcomes from which the
voters will be choosing.
134. Refer to Table 22-17. The table shows the preferences for three types of voters over three
possible outcomes: A, B, and C. The table also shows the percentage of voters of each type.
Based on this information, which of the following statements is true?
a. In a vote between B and C, C loses since only the Type 1 voters prefer C to B.
b. In a vote between A and B, B wins getting 85% of the total vote.
c. In a vote between A and C, C loses getting only 45% of the total vote.
d. Both a and b.
5508 Frontiers of Microeconomics
Table 22-18
The following table shows the preferences of four types of voters over four possible alternatives
as well as the percentage of the electorate with the given preferences.
Type 1
Type 2
Type 3
Type 4
Percent of voters
25
30
40
5
First choice
W
X
Y
Z
Second choice
X
Z
W
Y
Third choice
Y
W
Z
X
Fourth choice
Z
Y
X
W
135. Refer to Table 22-18. In a majority vote between alternatives W and X, what percentage of
the votes would W receive?
a. 35%
b. 45%
c. 55%
d. 65%
136. Refer to Table 22-18. In a majority vote between alternatives X and Y, what percentage of
the votes would X receive?
a. 35%
b. 45%
c. 55%
d. 65%
Frontiers of Microeconomics 5509
137. Refer to Table 22-18. Suppose voters first choose in a majority vote between W and X.
Second, voters choose in a majority vote between the winner of the first vote and Y. Third,
voters choose in a majority vote between the winner of the second vote and Z. Which alternative
will win?
a. W
b. X
c. Y
d. Z
138. Refer to Table 22-18. Suppose before any voting takes place that alternative W is eliminated
as an option. If the voters first choose between alternatives X and Y in a majority vote, with the
winner of that vote going against option Z in a majority vote, which alternative would win?
a. X
b. Y
c. Z
d. There would be no clear winner - alternatives X and Y would tie.
5510 Frontiers of Microeconomics
139. Refer to Table 22-18. Suppose before any voting takes place that alternative W is eliminated
as an option. Based on this information, the median voter’s first choice is
a. X
b. Y
c. Z
d. The median voter’s first choice cannot be determined from the information given.
140. Refer to Table 22-18. If the vote is conducted using a Borda count where each person’s first
choice receives 4 points, each person’s second choice 3 points, each person’s third choice 2
points, and each person’s fourth choice 1 point, which alternative would win?
a. W
b. X
c. Y
d. Z
Frontiers of Microeconomics 5511
Table 22-19
The 600 voters of Appleton are deciding by majority rule how much to spend on a new library.
Number of voters who most prefer this amount of spending
$0
50
$2 million
100
$3 million
125
$4 million
150
$5 million
175
141. Refer to Table 22-19. The median voter prefers to spend
a. $2 million.
b. $3 million.
c. $3.5 million.
d. $4 million.
142. Refer to Table 22-19. If an election were held between spending $2 million and $3 million, the
median voter would vote for
a. $3 million and $3 million would win.
b. $3 million and $2 million would win.
c. $2 million and $3 million would win.
d. $2 million and $2 million would win.
5512 Frontiers of Microeconomics
143. Refer to Table 22-19. If an election were held between spending $2 million and $4 million, the
median voter would vote for
a. $2 million and $2 million would win.
b. $2 million and $2 million would win.
c. $4 million and $2 million would win.
d. $4 million and $4 million would win.
Frontiers of Microeconomics 5513
Table 22-20
The table below shows the preferred city budget (in millions) for in the city of Springfield.
Percent of Voters
Preferred Budget
4%
$60
6%
$50
14%
$0
16%
$40
18%
$20
20%
$30
22%
$10
144. Refer to Table 22-20. In an election, each voter will select the budget closest to his or her
most preferred budget. Using this information, what is the most preferred budget of the median
voter?
a. $10
b. $20
c. $30
d. $40
5514 Frontiers of Microeconomics
145. Refer to Table 22-20. In an election, each voter will select the budget closest to his or her
most preferred budget. In which of the following cases does a budget of $32 win?
a. $32 versus $10, and $32 versus $40
b. $32 versus $10, but not $32 versus $40
c. $32 versus $40, but not $32 versus $10
d. Neither $32 versus $10 nor $32 versus $40
146. Refer to Table 22-20. In an election, each voter will select the budget closest to his or her
most preferred budget. In which of the following cases does a budget of $22 win?
a. $22 versus $10, and $22 versus $40
b. $22 versus $10, but not $22 versus $40
c. $22 versus $40, but not $22 versus $10
d. Neither $22 versus $10 nor $22 versus $40
Frontiers of Microeconomics 5515
Scenario 22-4
Three members of the DiCarlo family, Vinny, Maria, and Franki, are choosing the entree for a
large family reunion. Their options are: spaghetti, ravioli, lasagne, and pizza. Vinny prefers
spaghetti over lasagne, lasagne over ravioli, and ravioli over pizza. Maria prefers ravioli over
spaghetti, spaghetti over pizza, and pizza over lasagne. Frankie prefers pizza over ravioli, ravioli
over lasagne, and lasagne over spaghetti.
147. Refer to Scenario 22-4. Maria recommends using a vote by majority rule and proposes first
choosing between spaghetti and lasagne, then choosing between the winner of the first vote and
ravioli, and finally choosing between the winner of the second vote and pizza. If everyone votes
according to his or her preferences,
a. the winner of the first vote will be spaghetti, the winner of the second vote will be ravioli, and
the winner of the final vote will be ravioli.
b. the winner of the first vote will be spaghetti, the winner of the second vote will be spaghetti,
and the winner of the final vote will be spaghetti.
c. the winner of the first vote will be lasagne, the winner of the second vote will be ravioli, and
the winner of the final vote will be ravioli.
d. the winner of the first vote will be lasagne, the winner of the second vote will be lasagne, and
the winner of the final vote will be ravioli.
5516 Frontiers of Microeconomics
148. Refer to Scenario 22-4. Vinny recommends using a vote by majority rule and wants to be sure
that his first choice becomes the winner. Which order should he should propose to use for
pairwise voting to ensure his desired outcome?
a. first choosing between ravioli and spaghetti, then choosing between the winner of the first
vote and pizza, and finally choosing between the winner of the second vote and lasagne
b. first choosing between pizza and spaghetti, then choosing between the winner of the first vote
and lasagne, and finally choosing between the winner of the second vote and ravioli
c. first choosing between lasagne and pizza, then choosing between the winner of the first vote
and ravioli, and finally choosing between the winner of the second vote and spaghetti
d. None of the proposed voting orders will result in Vinny’s first choice winning the vote.
149. Refer to Scenario 22-4. 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 election winner would be
a. pizza.
b. ravioli.
c. lasagne.
d. spaghetti.
Frontiers of Microeconomics 5517
150. Refer to Scenario 22-4. If, before any votes were cast, ravioli was eliminated from the
choices and 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 election
winner would be
a. pizza.
b. spaghetti
c. lasagne.
d. The result would be a three-way tie between pizza, spaghetti and lasagne.
151. Refer to Scenario 22-4. If, before any votes were cast, ravioli was eliminated from the
choices, the median voter’s first choice would be
a. pizza.
b. spaghetti
c. lasagne.
d. There is not enough information to answer this question.
5518 Frontiers of Microeconomics
Table 22-21
The following table shows the number of voters preferring various amounts of spending to
develop a river to make it more attractive for canoeing and kayaking.
Number of Voters
Preferred Spending (millions)
1
$0.0
4
$0.5
20
$1.0
22
$1.5
25
$2.0
35
$2.5
15
$3.0
152. Refer to Table 22-21. What is the preferred spending amount of the median voter?
a. $1.0
b. $1.5
c. $2.0
d. None of the above are correct.
Frontiers of Microeconomics 5519
153. Refer to Table 22-21. Suppose the voters are asked to choose between $1 million and $2.5
million. If all voters cast a vote for the spending amount closest to their own preference, how
many votes will the $1 million spending amount receive?
a. 25
b. 47
c. 72
d. 102
154. Refer to Table 22-21. The city council is considering two alternative ballots. The first would
allow voters to choose between $1.5 million and $2 million. The second would allow voters to
select between $2 million and $2.5 million. If the first ballot is used,
a. voters will select $1.5 million. If the second ballot is used voters will select $2 million.
b. voters will select $1.5 million. If the second ballot is used voters will select $2.5 million.
c. voters will select $2 million. If the second ballot is used voters will select $2 million.
d. voters will select $2 million. If the second ballot is used voters will select $2.5 million
5520 Frontiers of Microeconomics
155. Refer to Table 22-21. Suppose on election day that the voters with a preference for less than
$1.5 million do not show up to vote on a choice to spend either $2 million or $2.5 million. In this
case, what is the preferred spending amount of the median voter (among those who actually cast
a vote)?
a. $2 million and $2 million wins.
b. $2 million, but $2.5 million wins.
c. $2.5 million, and $2.5 million wins.
d. $2.5 million, but $2 million wins.
Frontiers of Microeconomics 5521
Table 22-22
The town of Fairview is considering a renovation to the high school. The voters in Fairview have
different preferences on the budget for the renovation as displayed below.
Preferred Budget
Number of Voters
$0 million
12,000
$4 million
18,000
$8 million
6,000
$12 million
8,000
$16 million
19,000
$20 million
20,000
$24 million
10,000
156. Refer to Table 22-22. The median voter is one who prefers to spend
a. $12 million.
b. $16 million
c. $20 million.
d. None of the above are correct.
5522 Frontiers of Microeconomics
157. Refer to Table 22-22. If there is a vote between a budget of $16 million and $20 million and
voter vote for the budget nearest their preferred budget, then the median voter will vote to spend
a. $16 million and the voting outcome will be $16 million.
b. $16 million and the voting outcome will be $20 million.
c. $20 million and the voting outcome will be $20million.
d. $20 million and the voting outcome will be $20 million.
158. Refer to Table 22-22. If there is a vote between a budget of $12 million and $16 million, the
median voter will vote to spend
a. $12 million and the voting outcome will be $12 million.
b. $12 million and the voting outcome will be $16 million.
c. $16 million and the voting outcome will be $12 million.
d. $16 million and the voting outcome will be $16 million.
