Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
thumb_up100%
Chapter 1, Problem 1E
Figure 1-8 shows the preference ballots for an election with 21 voters and 5 candidates. Write out the preference schedule for this election.
Figure 1-8
Expert Solution & Answer
To determine
To find:
The preference schedule for the election with given preference ballots.
Answer to Problem 1E
Solution:
The preference schedule for the preference ballots for 21 voters and 5 candidates is,
| Number of Voters | 5 | 5 | 3 | 3 | 3 | 2 |
| 1st Choice | A | C | A | B | D | D |
| 2nd Choice | B | E | D | E | C | C |
| 3rd Choice | C | D | B | A | B | B |
| 4th Choice | D | A | C | C | E | A |
| 5th Choice | E | B | E | D | A | E |
Explanation of Solution
Given:
The preference ballots for 21 voters and 5 candidates are given as,
Calculation:
The ballots of the same preferences are grouped together as,
The preference schedule table for the above ballots is given by,
| Number of Voters | 5 | 5 | 3 | 3 | 3 | 2 |
| 1st Choice | A | C | A | B | D | D |
| 2nd Choice | B | E | D | E | C | C |
| 3rd Choice | C | D | B | A | B | B |
| 4th Choice | D | A | C | C | E | A |
| 5th Choice | E | B | E | D | A | E |
Conclusion:
The preference schedule for the preference ballots for 21 voters and 5 candidates is,
| Number of Voters | 5 | 5 | 3 | 3 | 3 | 2 |
| 1st Choice | A | C | A | B | D | D |
| 2nd Choice | B | E | D | E | C | C |
| 3rd Choice | C | D | B | A | B | B |
| 4th Choice | D | A | C | C | E | A |
| 5th Choice | E | B | E | D | A | E |
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Consider an election with 301 voters cast for 3 candidates. What is the smallest number of first-place votes that a candidate can receive to win by the Plurality method?
Determines who wins the plurality vote and who wins the rank voting or preferential voting
method in the election.
1. There are 650 students in a school, and they all get to vote for the school president. There are
3 candidates:
Rios,
• Millie,
• Charles.
Each student will receive a ballot and they will rank the candidates in or of 1", 2nd, and 3rd
choice. Remember on the preferential vote the winning candidate must have 1 more than
half the votes. See the results of the election below.
Votes
225
175
250
225
1¹
Millie
Charles
Rios
250
and
a. The person who has the largest number of first place votes is
b. The person who has the fewest number of first place votes is
c. The candidate we eliminate is
d. Fill in the new table.
1
Charles
Millie
Millie
Rios
Rios
Charles
2rd
Is there a majority of votes for a candidate now? If yes, who is that candidate, and
how many the first place votes does that candidate have?
f. Who won the plurality vote or single candidate voting method? Explain how…
Earlier we saw that Channel 6 News ran a poll on social media asking their followers to rank four local celebrities in order
from their favorite to least favorite. The preference schedule is given again below.
21
Number of Votes
1st choice
19
17
16
14
13
Leo
Mikey
Donnie
Leo
Mikey
Leo
Donnie
Raph
Donnie
Raph
Leo
2nd choice
Donnie
Leo
3rd choice
Mikey
Raph
Donnie
Mikey
Raph
Leo
Donnie
4th choice
Raph
Raph
Mikey
Mikey
This time, who should be proclaimed the Channel 6 News followers' favorite local celebrity if Copeland's Method is used?
Type your work and your answer below. Make sure to be detailed with your work.
Chapter 1 Solutions
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...
Additional Math Textbook Solutions
Find more solutions based on key concepts
38. Getting Hired The odds against Ishaq getting hired for a job are 3 : 8 Determine the probability
Ishaq gets...
A Survey of Mathematics with Applications (10th Edition) - Standalone book
43-44. Energy Savings. For these questions, assume 365 days in a year.
44. Suppose you have a clothes dryer t...
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
49-50. Energy Savings. For these questions, assume that there are
365 days in a year.
49. Your utility compan...
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
For Problems 23-28, write in simpler form, as in Example 4. logbFG
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
In using the technique of integration by parts, you must carefully choose which expression is u. For each of th...
Calculus Volume 2
Check Your Understanding
Reading Check Complete each sentence using > or < for □.
RC1. 3 dm □ 3 dam
Basic College Mathematics
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- This is not a graded question. The colored marked is for numbering.arrow_forwardVoting is done in a class consisting of 30 students to determine the study tour destination. One student may choose more than one tourist destination. Based on the choice of tours, it is known that A received a total of 9 votes, B 13 votes, C 7 votes, and D 9 votes. There are several students who choose 2 destinations at once, namely: 3 students choose A and B, 1 student chooses A and C, 4 students choose C and B. Draw the voting results in a venn diagram!arrow_forwardUse 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 1000 voters and the candidates need 501 to win. There are 4 candidates for the house of representatives and you have to rank them by preference. Votes 1st 2nd Зrd 4th 350 Emilio Howard Hannah Melissa 225 Howard Hannah Melissa Emilio 225 Melissa Hannah Howard Emilio 200 Hannah Howard Melissa Emilio a Preferential: Henry wins with 425, Plurality: Emilio wins with 350 Preferential: Howard wins with 575, Plurality: Emilio wins with 575 Preferential: Howard wins with 700, Plurality: Emilio wins with 350 d. Preferential: Howard wins with 650, Plurality: Emilio wins with 350 O O Oarrow_forward
- Compare and contrast the Borda count method and the purality-with-elimination method. Identify at least one similarity and one difference. Use a specific example of voting preferences to illustrate your point.arrow_forwardF959 - QUESTION 4. BORDA COUNT. The animals get sick and tired of having the Lion be the King of the Jungle, and they overthrow the Lion and hold an election for President of the Jungle. The candidates an the Zebra, the Elephant, the Baboon and the Hyena, and there are 67 voters. The 67 preference lists fall into 6 categories, as summarized below. Using the Borda count method, show the results of the election. 15 Zebra 13 Baboon 12 Zebra 10 Elephant Elephant Hyena 4₂15760 4•13=524.12 48 4.10€ 40 4x936 4×8=33 Hyena Hyena Baboon Hyena Elephant 3-15-45 3-13-39 3·12-30 3·10-30 3x9-27) 3x 8-24 Baboon Zebra Baboon Elephant 1.13 €13/1•12= 12 1·10 = (10) 9 Baboon Zebra Hyena Elephant Elephant Zebra 215- (30) 2.13 (24) 2-12 (24) 2·10 -(20) 2×9=182x8=16) Baboon Zebra 1.15-(15 Hyena 8 1x9 ✓9-9 1x8=8arrow_forwardQ1arrow_forward
- Answer numbers 2-4arrow_forwardIf you use plurality method. whose restaurant will win? Johnny Joey Rina Anna If you use plurality with elimination method (Hare System), whose restaurant will win? Johnny Joey Rina Annaarrow_forwardUse the Condorcet method to determine the winner of the election. Four students are running for president of the school: • Ariana (A), • Brett (B), • Carlos (C), and • DeeDee (D). The 5 clubs and their members were asked to rank all candidates. Number of Voters Preference Order 1st to last 19 A C D 15 В D A C 11 D A C В 7 D В A D A В a A b В C d No Condorcet winner O O O Oarrow_forward
- explain why when there are only two candidates, the four voting methods discussed give the same winner and the winner is determined by straight majority?arrow_forwardTo decide on a movie to watch, a group of friends all vote for one of the choices (labeled A, B. and C). The individual ballots are shown below. САВ, СВА, ВАС, ВСА, СВА, АВС, АВС, СВА, ВСА, САв, САВ, ВАС Create a preference table showing the results of the election.arrow_forwardThe students in a class get to decide on the color of the classroom. The two choices are blue and yellow. Polling shows yellow is preferred by a small majority, 53% for yellow to 47% for blue. However, before the vote is held, a new color choice is added: red. Not a lot of people like red, but there are some yellow supporters who would actually vote for red. The results of the vote are below. Blue Yellow Red 46% 44% 10% What statement below is correct about adding a third choice to the plurality vote? O a Ob Oc d Red did not win the vote, but it draws enough support away from yellow to make blue the winner, even though a majority of students preferred yellow over blue when there were two choices. Red did not win the vote, but it had no effect on drawing enough support away from yellow to make blue the winner, even though a majority of students preferred yellow over blue when there were two choices. Red did not win the vote, so because of this, yellow should win the vote over blue.…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSON
Discrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License