EXCURSIONS IN MODERN MATH
5th Edition
ISBN: 9781323741559
Author: Tannenbaum
Publisher: PEARSON C
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Textbook Question
Chapter 1, Problem 39E
Top-Two Instant-Runoff Voting. Exercises 39 and 40 refer to a simple variation of the plurality-with-elimination method called top-two IRV. This method works for winner-only elections. In top-two IRV, instead of eliminating candidates one at a time, we eliminate all the candidates except the top two in the first round and transfer their votes to the two remaining candidates.
Find the winner of the election given in Table 1-39 using the top-two IRV method.
Table 1-39
Number of Voters | 8 | 7 | 5 | 4 | 3 | 2 |
1st | B | C | A | D | A | D |
2nd | E | E | B | C | D | B |
3rd | A | D | C | B | E | C |
4th | C | A | D | E | C | A |
5th | D | B | E | A | B | E |
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What method of voting is described below?A single-winner electoral system where each voter may select any number of candidates. The winner is the most-approved candidate.
a
Plurality with elimination
b
Two-round runoff
c
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d
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Use the preferential voting method to determine the winner and compare it to the single candidate voting or plurality method. Who wins the
preferential vote and the single candidate vote?
There are 2000 voters and the candidates need 1001 to win. There are
candidates for the house of representatives and you have to rank
them by preference.
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1st
2nd
3rd
4th
630
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Henry
600
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Henry
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a
Preferential: Henry wins with 770, Plurality: Mary wins with 630
Preferential: Jazmine wins with 1370, Plurality: Mary wins with 700
Preferential: Jazmine wins with 970, Plurality: Mary wins with 630
d
Preferential: Jazmine wins with 1370, Plurality: Mary wins with 630
O O O O
Use the preferential voting method to determine the winner and compare it to the single candidate voting or plurality method. Who wins the
preferential vote and the single candidate vote?
There are 2000 voters and the candidates need 1001 to win. There are 4 candidates for the house of representatives and you have to rank
them by preference.
Votes
1st
2nd
3rd
4th
630
Mary
Jazmine
Marcos
Henry
600
Jazmine
Marcos
Henry
Mary
400
Henry
Marcos
Jazmine
Mary
370
Marcos
Jazmine
Henry
Mary
a. Preferential: Henry wins with 770, Plurality: Mary wins with 630
b. Preferential: Jazmine wins with 1370, Plurality: Mary wins with 700
c. Preferential: Jazmine wins with 970, Plurality: Mary wins with 630
d. Preferential: Jazmine wins with 1370, Plurality: Mary wins with 630
Chapter 1 Solutions
EXCURSIONS IN MODERN MATH
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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- Use the sequential runoff method to determine the winner of the election if a majority winner cannot be determined. Votes 7 8 6. 5 1st Place A В 2nd Place В C В В 3rd Place 4th Place D A A A a A В C d. O O O Oarrow_forwardUse the plurality with elimination method to determine the winner and compare it to the plurality method. Who wins the preferential vote and the single candidate vote? There are 74 voters and the candidates need 37 votes to win. There are 5 candidates for the house of representatives and you have to rank them by preference. Votes 20 16 12 15 11 1st Emilio Howard Richard Melissa Hannah 2nd Howard Melissa Hannah Hannah Emilio 3rd Melissa Emilio Melissa Richard Richard 4th Hannah Richard Emilio Howard Howard 5th Richard Hannah Howard Emilio Melissa a Plurality with elimination: Richard wins with 43, Plurality: Emilio wins with 20 Plurality with elimination: Melissa wins with 43, Plurality: Emilio wins with 20 Plurality with elimination: Hannah wins with 43, Plurality: Emilio wins with 20 d. Plurality with elimination: Emilio wins with 37, Plurality: Emilio wins with 20arrow_forwardFour candidates, Lito, Quennie, Kyleigh, and Irish are running for president of the student government. After the polls close, votes are tallied, and the results in the table below are obtained. Candidate Lito Quennie Kyleigh IrishNumber of Votes 314 155 1,052 479 How many votes were cast? Using the plurality method of voting, who wins the election?Did the winner receive a majority of the votes? Why?arrow_forward
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