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.

Accepted Answer

The head-to-head comparison criterion is violated if the candidate who wins the election by plurality does not win in a head-to-head comparison against at least one other candidate. In this case, X is the plurality winner with five first-place votes, but in a head-to-head comparison against Z, X only receives three votes compared to Z's four votes. Therefore, the head-to-head comparison criterion has been violated.

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.

Accepted Answer

The Borda count method assigns points to each option based on their position in the preference list. The first choice receives 3 points, the second choice receives 2 points, and the third choice receives 1 point. The fourth choice, which is the least preferred option, receives 0 points.

Using this method, we can calculate the total points for each option:
- 12:00 p.m.: 0 + 1 + 3 + 0 = 4
- 1:00 p.m.: 0 + 1 + 2 + 3 = 6
- 5:00 p.m.: 2 + 3 + 1 + 1 = 7
- 6:00 p.m.: 1 + 2 + 0 + 2 = 5

Therefore, the option with the highest total points is 5:00 p.m., making it the winner according to the Borda count method. However, it's worth noting that there is a tie for the best choice between 5:00 p.m. and 1:00 p.m., as they are only separated by one point. Using the Borda count method, each choice receives a certain number of points depending on its ranking. The choice with the highest total number of points is the winner. 
In this case, each first place vote receives 3 points, each second place vote receives 2 points, each third place vote receives 1 point, and each last place vote receives 0 points. 
Calculating the total points for each choice: 
- 12:00 p.m.: 28 points 
- 1:00 p.m.: 31 points 
- 5:00 p.m.: 37 points 
- 6:00 p.m.: 43 points 
Therefore, the choice with the highest total points and thus the winner is 6:00 p.m. (Option 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.

Accepted Answer

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

Question 4

Make a preference table for the following preference ballots.

Accepted Answer

The answer of Make a preference table for the following...

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.

Accepted Answer

The answer of The results of an election are summarized...

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.

Accepted Answer

The answer of The Ballroom Dance Club voted on what...

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?

Accepted Answer

The answer of Use a preference table for the following...

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)

Accepted Answer

The answer of A class of fifth graders voted on...

Question 9

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

Accepted Answer

The answer of The preference table below summarizes the results...

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

Accepted Answer

Using the plurality method, we simply count the number of first place votes each candidate received. 
P: 4
J: 3
K: 2
Therefore, P has the most first place votes and is the winner. According to the plurality method, the candidate with the most first-place votes wins. In this case, P has 6 first-place votes, while K, J, and T have 4, 3, and 2 first-place votes respectively. Therefore, P is the winner.

Question 11

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

Accepted Answer

The answer of Use a preference table for the following...

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.

Accepted Answer

The answer of Mrs. Jackson's third-grade class voted on whether...

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

Accepted Answer

The answer of The preference table below summarizes the results...

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.

Accepted Answer

The answer of The results of an election are summarized...

Question 15

Make a preference table for the following preference ballots.

Accepted Answer

The answer of Make a preference table for the following...

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?

Accepted Answer

The answer of Use a preference table for the following...

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?

Accepted Answer

The answer of Use the plurality method to determine the...

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.

Accepted Answer

The answer of Use a preference table for the following...

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.

Accepted Answer

The answer of  The results of an election are...

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.

Accepted Answer

The answer of A homeowners association voted on what color...

Quiz 12: Voting Methods

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 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.

Make a preference table for the following preference ballots.

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.

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?

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.

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

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

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

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

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.

Make a preference table for the following preference ballots.

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?

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?

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

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.