Excursions in Modern Mathematics, Books a la Carte Edition Plus MyLab Math -- Access Card Package (9th Edition)
9th Edition
ISBN: 9780134765839
Author: Peter Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 1, Problem 18E
Table 1-26 (see Exercise 4) shows the preference schedule for an election with five candidates (A, B, C and D). In this election ties are not allowed to stand, and the following tie-breaking rule is used: Whenever there is a tie between candidates, the tie is broken in favor of the candidate with the fewer last-place votes. Use the plurality method to
a. find the winner of the election.
b. find the complete ranking of the candidates.
Table 1-26
| Number of voters | 202 | 160 | 153 | 145 | 125 | 110 | 108 | 102 | 55 |
| 1st | B | C | A | D | D | C | B | A | A |
| 2nd | D | B | C | B | A | A | C | B | D |
| 3rd | A | A | B | A | C | D | A | D | C |
| 4th | C | D | D | C | B | B | D | C | B |
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Students have asked these similar questions
The results of an election are summarized in the following preference table. Determine the winner using the plurality method.
The results of an election are summarized in the following preference table. Determine the winner using the Borda Count method.
Consider the preference table below for an election.
First
A
B
C
Second
B
C
A
Third
C
A
B
Votes
11
7
5
(c) A second election is held and candidate B drops out but voters do not change their preferences, Redraw the Preference schedule with candidate B removed.
(d) Find the winner of the preference (redrawn) schedule using the points method.
Chapter 1 Solutions
Excursions in Modern Mathematics, Books a la Carte Edition Plus MyLab Math -- Access Card Package (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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- Twenty−three members of the executive committee of the Student Senate must vote for a student representative for the college board of trustees from among three candidates: Greenburg (G), Haskins (H), and Vazquez (V). The preference table follows. Number of Votes 9 2 8 4 First V G H H Second G H V G Third H V G V Another way to determine the winner if the plurality with elimination method is used is to eliminate the candidate with the most last-place votes at each step. Using the preference table given to the left, determine the winner if the plurality with elimination method is used and the candidate with the most last-place votes is eliminated at each step. Choose the correct answer below. A. Haskins B. Greenburg C. Vazquez D. There is no winner. There is a tie between Vazquez and Greenburg. E. There is no winner. There is a three-way tie.arrow_forwardTwenty−one members of the executive committee of the Student Senate must vote for a student representative for the college board of trustees from among three candidates: Greenburg (G), Haskins (H), and Vazquez (V). The preference table follows. Number of Votes 8 2 7 4 First H V G G Second V G H V Third G H V H ..... Another way to determine the winner if the plurality with elimination method is used is to eliminate the candidate with the most last-place votes at each step. Using the preference table given to the left, determine the winner if the plurality with elimination method is used and the candidate with the most last-place votes is eliminated at each step. Choose the correct answer below. A. Greenburg B. Vazquez C. Haskins D. There is no winner. There is a tie between Haskins and Vazquez. E. There is no winner. There is a three-way tie.arrow_forward12. Use the following preference schedule to answer the following question: Which of the candidates was the Majority candidate?arrow_forward
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