Deck 12: Voting Methods

Question 1

The results of an election are summarized in the following preference table. If the plurality method
Is used, determine whether the head-to-head comparison criterion has been violated and explain
Why.

A)Yes, because X does not win over Y in a head-to-head comparison.
B)No, because X wins over Y and Z in a head-to-head comparison.
C)No, because X is the plurality winner.
D)Yes, because X does not win over Z in a head-to-head comparison.

Answer 1

D

Question 2

A club voted on what time to have their next meeting (12:00 p.m., 1:00 p.m., 5:00 p.m., or 6:00
P.m.). The election results are summarized in the preference table below. Using the Borda count method of voting, determine the winner.

A)5:00 p.m.
B)6:00 p.m.
C)1:00 p.m.
D)12:00 p.m.

Answer 2

B

Question 3

The preference ballots for the election of teacher of the year by a junior high school are shown below. Make a
preference table for the results of the election and answer each question.
(a)How many people voted?
(b)How many people voted for the candidates in the order of preference BTW?
(c)How many people voted for candidate B as their first choice?
(d)Using the plurality method, determine the winner of the election.

Answer 3

(a)22
(b)8
(c)10
(d)Tie between B and T

Question 4

Make a preference table for the following preference ballots.

Question 5

The results of an election are summarized in the following preference table. Determine the winner
using the plurality method. Then decide whether the election violates the head-to-head comparison
criterion and explain your answer.

Question 6

The Ballroom Dance Club voted on what time to have their Saturday meetings: 9:00 a.m. (N), 10:00 a.m. (T),
or 11:00 a.m. (E). The preference ballots for the election are shown below. Make a preference table for the
results of the election and answer each question.
(a)How many people voted?
(b)How many people voted for the candidates in the order of preference NTE?
(c)How many people voted for candidate N as their first choice?
(d)Using the plurality method, determine the winner of the election.

Question 7

Use a preference table for the following preference ballots to answer the questions. (a)How many people voted?
(b)How many people voted for the candidates in the order of preference XYZ?
(c)How many people voted for candidate Y for their first choice?

Question 8

A class of fifth graders voted on their favorite flavor of ice cream, vanilla (V), chocolate (C), or
Strawberry (S). The election results are summarized in the preference table below. Using the Borda count method of voting, determine the winner.

A)Vanilla (V)
B)Strawberry (S)
C)Chocolate (C)

Question 9

The preference table below summarizes the results of an election. Use the Borda count method of
voting, determine the winner.

Question 10

The results of an election are summarized in the following preference table. Determine the winner
Using the plurality method.

A)Tie between P and J
B)K
C)J
D)P

Question 11

Use a preference table for the following preference ballots to determine the winner using the
plurality method.

Question 12

Mrs. Jackson's third-grade class voted on whether to have a clown (C), a magician (M), or a superhero (S)at
their class party. Their preference ballots are shown below. Make a preference table for the results of the
election and answer each question.
(a)How many people voted?
(b)How many people voted for the candidates in the order of preference MSC?
(c)How many people voted for candidate C as their first choice?
(d)Using the plurality method, determine the winner of the election.

Question 13

The preference table below summarizes the results of an election. Using the Borda count method of voting, determine the winner.

A)K
B)J
C)F
D)T

Question 14

The results of an election are summarized in the following preference table. If the plurality method
Is used to determine the winner, decide whether the head-to-head comparison criterion has been
Violated and explain your answer.

A)Yes. In a head-to-head comparison I won over Y but lost to E.
B)Yes. In a head-to-head comparison I won over E but lost to Y.
C)No. I is the plurality winner.
D)No. In a head-to-head comparison I won over Y and E.

Question 15

Make a preference table for the following preference ballots.

Question 16

Use a preference table for the following preference ballots to answer the questions. (a)How many people voted?
(b)How many people voted for the candidates in the order of preference BCA?
(c)How many people voted for candidate B for their first choice?

Question 17

Use the plurality method to determine the winner of the election summarized in the following
preference table. Has the head-to-head comparison criterion been violated?

Question 18

Use a preference table for the following preference ballots to determine the winner of the election
Using the plurality method.

A)Candidate A wins.
B)Candidate C wins.
C)Candidate B wins.
D)Candidates A and B tie.

Question 19

The results of an election are summarized in the following preference table.
(a)How many people voted?
(b)Determine the winner using the plurality method.

Question 20

A homeowners association voted on what color to paint the clubhouse, white (W), yellow (Y), or
taupe (T). The preference ballots for the election are shown below. Make a preference table for the
results of the election and answer each question.
(a)How many people voted?
(b)How many people voted for the candidates in the order of preference WYT?
(c)How many people voted for candidate W as their first choice?
(d)Using the plurality method, determine the winner of the election.

Question 21

The preference table below summarizes the results of an election. (a)Using the Borda count method of voting, determine the winner.
(b)Does the election violate the majority criterion?

Question 22

The preference table below summarizes the results of an election. (a)Using the Borda count method of voting, determine the winner.
(b)Does the election violate the majority criterion?

Question 23

If there are 8 candidates in an election, how many pairwise comparisons need to be made in order to
Determine a winner?

A)28
B)8
C)36
D)56

Question 24

The math department is voting for a new department chairperson. The candidates are Jenkins (J),
Peterson (P), and Thomas (T). The results of the election are summarized in the preference table
Below. Using the plurality-with-elimination method of voting, determine the winner.

A)Thomas (T)
B)Peterson (P)
C)Jenkins (J)

Question 25

Suppose the election is declared invalid, and a reelection is held in which the people who originally
voted XWYZ change their vote to ZWYX. Is the monotonicity criterion violated? Explain your answer.

Question 26

The results of an election are summarized in the preference table below. Using the pairwise comparison voting method, determine the winner.

A)C
B)A
C)B

Question 27

The results of an election are summarized in the following preference table. (a)Determine the winner using the Borda method of voting.
(b)Is the winner the same as the one determined by the plurality method?

Question 28

The results of an election are summarized in the preference table below. Using the plurality-with-elimination method of voting, determine the winner.

A)A
B)D
C)C
D)B

Question 29

The results of an election are summarized in the preference table below. Using the plurality-with-elimination method of voting, determine the winner.

A)Y
B)X
C)W
D)Z

Question 30

The results of an election are summarized in the preference table below. Suppose the election is declared invalid, and a reelection is held. If the people who voted XYZ in the
Original election change their vote to ZXY, is the monotonicity criterion violated?

A)Yes
B)No

Question 31

A club voted on what time to have their next meeting (12:00 p.m., 1:00 p.m., 5:00 p.m., or 6:00
p.m.). The election results are summarized in the preference table below. Does the election violate the majority criterion? Explain your answer.

Question 32

If there are 4 candidates in an election, how many pairwise comparisons need to be made in order to
determine a winner?

Question 33

The results of an election are summarized in the preference table below. Using the plurality-with-elimination method of voting, determine the winner.

A)A
B)D
C)C
D)B

Question 34

A class of fifth graders voted on their favorite flavor of ice cream, vanilla (V), chocolate (C), or
strawberry (S). The election results are summarized in the preference table below. Does the election violate the majority criterion? Explain your answer.

Question 35

The results of an election are summarized in the preference table below. If candidate A is unable to serve in the election and the votes are recounted, does this election violate the
irrelevant alternative criterion? Explain your answer.

Question 36

The results of an election are summarized in the preference table below. Using the pairwise comparison voting method, determine the winner.

Question 37

The math department is voting for a new department chairperson. The candidates are Jenkins (J),
Peterson (P), and Thomas (T). The results of the election are summarized in the preference table
Below. The winner is determined by the plurality-with-elimination method.
Suppose the election is declared invalid, and that a reelection is held. If the voters in column 2 change their
Vote from JPT to PJT, is the monotonicity criterion violated?

A)Yes
B)No

Question 38

The results of an election are summarized in the preference table below. The winner is determined using the plurality-with-elimination method.
Suppose the election is declared invalid. The results of the reelection are summarized in the preference table
below. Is the monotonicity criterion violated? Explain your answer.

Question 39

The results of an election are summarized in the preference table below. Using the plurality-with-elimination method of voting, determine the winner.

A)X
B)Z
C)Y

Question 40

The results of an election are summarized in the following preference table. (a)Determine the winner using the Borda method of voting.
(b)Is the winner the same as the one determined by the plurality method?

Question 41

A department store is hiring 13 new sales associates and needs to assign them to four departments
According to the volume of sales in dollars. The daily sales in dollars are given below. (a)Use the
Huntington-Hill method to decide how many associates each department should receive and (b)write the (standard or modified)divisor used (answers may vary). Round divisor to the nearest
Whole number.

A)
B)
C)
D)

Question 42

Twelve new police officers are to be assigned to four precincts. The populations of the precincts are
Shown below. (a)Use Webster's method to determine how many of the 12 new officers each
Precinct should receive and (b)write the modified divisor used (answers may vary). Round the
Divisor to the nearest whole number, if necessary.

A)
B)
C)
D)

Question 43

The results of an election are summarized in the preference table below. (a)Using the pairwise comparison voting method, determine the winner.
(b)If candidate Z drops out, does this election violate the irrelevant alternative criterion?

Question 44

The results of an election are summarized in the preference table below. (a)Using the pairwise comparison voting method, determine the winner.
(b)If candidate X drops out and the votes are recounted, does this election violate the irrelevant alternative
Criterion?

Question 45

A city with three districts has an increase in population as indicated in the table, Using Hamilton's
Method, apportion the 21 seats between the three districts both before and after the population
Increase. Look at the percent increase in population for each district to determine if the population
Paradox occurred.

A)population paradox occurred
B)population paradox did not occur

Question 46

A committee must select one of its members to serve as president. They vote using the approval
Method. The results are shown. Who was selected to be president of the committee?

A)Kim
B)Morgan
C)Bayer
D)Nelson

Question 47

A large chain store needs to assign 11 buyers to its five stores. The standard divisor is 29.7 and the
Number of employees and standard quota for each store are shown below. (a)Determine how many
Buyers each store should receive using Jefferson's method and (b)indicate the modified divisor used
(answers may vary). Round the divisor to the nearest tenth, if necessary.

A)
B)
C)
D)

Question 48

A club voted on whether to meet on Monday (M), Wednesday (W), Friday (F), or Saturday (S). The
Results of the election are summarized in the preference table below. (a)Using the pairwise comparison voting method, determine the winner.
(b)If candidate S is eliminated and the votes are recounted, does this election violate the irrelevant alternative
Criterion?

Question 49

A freight company has four terminals. The volume of business in truckloads for each terminal is
Shown below along with the standard quota. The owner has purchased 9 new trucks to be allocated
To the four terminals. If the standard divisor is 20.8, (a)determine how many trucks each terminal
Should receive using Adam's method and (b)indicate the modified divisor used (answers may vary).
Round the divisor to the nearest tenth, if necessary.

A)
B)
C)
D)

Question 50

The table shows the enrollment at two campuses of a community college. (a)Apportion 55 new media podiums to the two campuses according to Hamilton's method.
(b)Suppose the college adds a third campus with enrollment of 1,143 and correspondingly adds seven
Podiums. Reapportion the 62 podiums using Hamilton's method.
(c)Determine if the new states paradox occurs.

A)
B)
C)
D)

Question 51

The results of an election are summarized in the preference table below. (a)Using the pairwise comparison voting method, determine the winner.
(b)If candidate B is eliminated and the votes are recounted, does this election violate the irrelevant alternative
Criterion?

Question 52

A tenure board must select one teacher to get tenure. They vote using the approval method. The
Results are shown. Which teacher was selected?

A)Sykes
B)Draper
C)Robins
D)Wong

Question 53

A hiring board must select a new teacher. They vote using the approval method. The results are
Shown. Which applicant was selected?

A)Boyd
B)Phillips
C)James
D)Hanson

Question 54

This year 10 faculty members are to receive promotions at a community college with three
Campuses. The number of promotions will be apportioned according to the number of full-time
Faculty members as shown. Find (a)the standard divisor and (b)the standard quota for each district.
Round answers to three decimal places, if necessary.

A)(a)45
B)(a)46
C)(a)46
D)(a)45 (b)South: 2.956 (b)South: 2.956 (b)South: 2.891 (b)South: 2.891
Central: 3.2 Central: 3.2 Central: 3.13 Central: 3.13
North: 3.844 North: 3.844 North: 3.761 North: 3.761

Question 55

A county library has three branches. The number of books at each branch of the library is shown
Below. The head librarian purchased 53 new books and apportioned them to the libraries using
Hamilton's method. When the book order arrived the librarian noticed there was an extra book
Added as a "bonus" and she reapportioned the books with the extra book added. Determine if the
Reapportionment resulted in the Alabama paradox

A)Alabama paradox did not occur
B)Alabama paradox occurred

Question 56

A county has three clinics; the weekly number of patients seen by a nurse practitioner in each clinic
Is shown below. The director hires eight new nurse practitioners; find the geometric mean of the
Upper and lower quotas for each clinic. Round to three decimal places, if necessary.

A)
B)
C)
D)

Question 57

An automotive repair company has four stores in a large city. The owner purchased 7 diagnostic
Computers for the business. The number of cars serviced per store each month is given below along
With the standard quota. If the standard divisor is 79.7, (a)use Webster's method to determine how
Many computers each store should get based on number of cars serviced and (b)write the modified
Divisor used (answers may vary). Round the divisor to the nearest tenth, if necessary.

A)
B)
C)
D)

Question 58

A county has three districts. Seven representatives are to be appointed to the county board. The
Standard divisor is 65 and the standard quota for each district is shown below. (a)Find the upper
And lower quotas for each district and (b)determine how many representatives each district should
Receive using Hamilton's method.

A)
B)
C)
D)