MyLab Math with Pearson eText -- Standalone Access Card -- for Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134751818
Author: Peter Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 1, Problem 45E
Table 1-35 (see Exercise 15) shows the preference schedule for an election with five candidates (A, B, C, D, and E). The number of voters in this election was very large, so the columns of the preference schedule give percent of voters instead of the numbers of voters. Find the winner of election using the method of pairwise comparisons.
Percent of voters |
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|
|
|
|
|
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C | D | D | B | A | D |
|
A | A | A | C | C | C |
|
B | C | E | A | B | A |
|
E | B | C | D | E | E |
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D | E | B | E | D | B |
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Check out a sample textbook solutionStudents have asked these similar questions
A senior high school class held an election for class president. Instead of just voting for one candidate, the students were asked to rank all four candidates in order of preference. The results are shown in the table below.
Rankings
Raymond Lee
2
3
1
3
4
2
Suzanne Brewer
4
1
3
4
1
3
Elaine Garcia
1
2
2
2
3
4
Michael Turley
3
4
4
1
2
1
Number of votes:
12
21
17
26
18
16
Using the Borda Count method, which student should be class president?
The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference table below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S).
Number of Votes 7 10 4 8
First J S J C
Second S J C S
Third C C S J
Determine the winner using the pairwise comparison method. Did the winner receive a majority of the first place votes using the pairwise comparison method?
Select one:
a.
Clark; Yes
b.
Smith; Yes
c.
Smith; No
d.
Clark; No
e.
Jones; No
f.
Jones; Yes
Here is the preference schedule for a recent election among four candidates:
Number of voters
11
7
5
9
2
18
1
1st choice
K
B
B
G
A
B
A
2nd choice
G
A
G
A
B
K
G
3rd choice
B
K
A
K
G
A
K
4th choice
A
G
K
B
K
G
B
How many voters voted in this election? How many first place votes are needed for a majority? Which candidate/choice had the most first-place votes? Which candidate/choice has the least first-place votes? Which candidate/choice had the most last-place votes? Which candidate/choice has the least last-place votes?
Chapter 1 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Excursions in Modern Mathematics (9th Edition)
Ch. 1 - Figure 1-8 shows the preference ballots for an...Ch. 1 - Figure 1-9 shows the preference ballots for an...Ch. 1 - An election is held to choose the Chair of the...Ch. 1 - The student body at Eureka High School is having...Ch. 1 - An election is held using the printed-names format...Ch. 1 - Prob. 6ECh. 1 - Prob. 7ECh. 1 - Table 1-30 shows a conventional preference...Ch. 1 - The Demublican Party is holding its annual...Ch. 1 - The Epicurean Society is holding its annual...
Ch. 1 - Table 1-31 shows the preference schedule for an...Ch. 1 - Table 1-32 shows the preference schedule for an...Ch. 1 - Table 1-33 shows the preference schedule for an...Ch. 1 - Table 1-34 shows the preference schedule for an...Ch. 1 - Table 1-35 shows the preference schedule for an...Ch. 1 - Table1-36 shows the preference schedule for an...Ch. 1 - Table 1-25 see Exercise 3 shows the preference...Ch. 1 - Table 1-26 see Exercise 4 shows the preference...Ch. 1 - Table 1-25 see Exercise 3 shows the preference...Ch. 1 - Table 1-26 see Exercise 4 shows the preference...Ch. 1 - Table 1-31see Exercise 11 shows the preference...Ch. 1 - Table 1-32 see Exercise 12 shows the preference...Ch. 1 - Table 1-33 see Exercise 13 shows the preference...Ch. 1 - Table 1-34 Number of voters 6 6 5 4 3 3 1st A B B...Ch. 1 - Table 1-35 Percent of voters 24 23 19 14 11 9 1st...Ch. 1 - Table 1-36 Percent of voters 25 21 15 12 10 9 8...Ch. 1 - The Heisman Award. Table 1-37 shows the results...Ch. 1 - The 2014 AL Cy Young Award. Table 1-38 shows the...Ch. 1 - An election was held using the conventional Borda...Ch. 1 - Imagine that in the voting for the American League...Ch. 1 - Table 1-31 see Exercise 11 shows the preference...Ch. 1 - Table 1-32 see Exercise 12 shows the preference...Ch. 1 - Table1-33 Number of voters 6 5 4 2 2 2 2 1st C A B...Ch. 1 - Table 1-34 See Exercise 14 shows the preference...Ch. 1 - Table1-39_ shows the preference schedule for an...Ch. 1 - Table1-40_ shows the preference schedule for an...Ch. 1 - Table 1-35 see Exercise 15 shows the preference...Ch. 1 - Table 1-36 see Exercise 16 shows the preference...Ch. 1 - Top-Two Instant-Runoff Voting. Exercises 39 and 40...Ch. 1 - Top-Two Instant-Runoff Voting. Exercises 39 and 40...Ch. 1 - Table 1-31 see Exercise 11 shows the preference...Ch. 1 - Table 1-32 See Exercise 12 shows the preference...Ch. 1 - Table 1-33 see Exercise 13 shows the preference...Ch. 1 - Table 1-34 see Exercise 14 shows the preference...Ch. 1 - Table 1-35 see Exercise 15 shows the preference...Ch. 1 - Table 1-36 see Exercise 16 shows the preference...Ch. 1 - Table 1-39 see Exercise 35 shows the preference...Ch. 1 - Table1-40 see Exercise36 shows the preference...Ch. 1 - An election with five candidates A, B. C, D, and E...Ch. 1 - An election with six candidates A, B, C, D, E, and...Ch. 1 - Use Table 1-41 to illustrate why the Borda count...Ch. 1 - Use Table 1-32 to illustrate why the...Ch. 1 - Use Table 1-42 to illustrate why the plurality...Ch. 1 - Use the Math Club election Example 1.10 to...Ch. 1 - Use Table 1-43 to illustrate why the...Ch. 1 - Explain why the method of pair wise comparisons...Ch. 1 - Prob. 57ECh. 1 - Explain why the plurality method satisfies the...Ch. 1 - Explain why the Borda count method satisfies the...Ch. 1 - Explain why the method of pairwise comparisons...Ch. 1 - Two-candidate elections. Explain why when there...Ch. 1 - Alternative version of the Borda count. The...Ch. 1 - Reverse Borda count. Another commonly used...Ch. 1 - The average ranking. The average ranking of a...Ch. 1 - The 2006 Associated Press college football poll....Ch. 1 - The Pareto criterion. The following fairness...Ch. 1 - The 2003-2004 NBA Rookie of the Year vote. Each...Ch. 1 - Top-two IRV is a variation of the...Ch. 1 - The Coombs method. This method is just like the...Ch. 1 - Bucklin voting. This method was used in the early...Ch. 1 - The 2016 NBA MVP vote. The National Basketball...Ch. 1 - The Condorcet loser criterion. If there is a...Ch. 1 - Consider the following fairness criterion: If a...Ch. 1 - Suppose that the following was proposed as a...Ch. 1 - Consider a modified Borda count where a...
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- A senior high school class held an election for class president. Instead of just voting for one candidate, the students were asked to rank all four candidates in order of preference. The results are shown in the table below. Rankings Raymond Lee 2 3 1 3 4 2 Suzanne Brewer 4 1 3 4 1 3 Elaine Garcia 1 2 2 2 3 4 Michael Turley 3 4 4 1 2 1 Number of votes: 26 21 22 23 19 24 Using the Borda Count method, which student should be class president? Raymond Lee Suzanne Brewer Elaine Garcia Michael Turleyarrow_forwardA chapter of the Sierra Club is voting for president. The candidates are (A)lvaro, (B)rown, (C)lark,and (D)ukevitch. Number of ballots 4 23 8 3 12 1st preference C D C A A 2nd preference A A B D B 3rd preference B B D B C 4th preference D C A C D Use the preference table to determine the winner using the Borda count method.arrow_forwardA senior high school class held an election for class president. Instead of just voting for one candidate, the students were asked to rank all four candidates in order of preference. The results are shown below. Rankings Raymond Lee 2 3 1 3 4 2 Suzanne Brewer 4 1 3 4 1 3 Elaine Garcia 1 2 2 2 3 4 Michael Turley 3 4 4 1 2 1 Number of votes: 39 52 40 25 31 42 Using the Borda count method, does the winner satisfy the majority criterion? Yes. Using the Borda count method, Elaine Garcia won the election, and she had a majority of first-place votes. Yes. Using the Borda count method, Raymond Lee won the election, and he had a majority of first-place votes. No. Using the Borda count method, Raymond Lee won the election, although Elaine Garcia had a majority of first-place votes. No. Using the Borda count method, Elaine Garcia won the election, although no candidate received a majority of first-place votes. No. Using the Borda count method, Raymond Lee won the…arrow_forward
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