Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
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 |
|
|
|
|
|
|
|
|
C | D | D | B | A | D |
|
|
A | A | A | C | C | C |
|
|
B | C | E | A | B | A |
|
|
E | B | C | D | E | E |
|
|
D | E | B | E | D | B |
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Mr. Abdul Rheman's class held an election for class president. Instead of just voting for one candidate, students need to rank all the
candidates according to their preference. The results are shown below:
Rankings
X
3
2
1
3
1
Y
2
2
1
3
1
3
1
2
Number of
8
7
8
6
7
Students
If you will use Borda Count Method, wherein the assigned points for 1st, 2nd and 3rd place are 3pts, 2pt, and 1pt respectively, who
will be the class president of Mr. Abdul Rheman and by how much points?
A Senior High School class held an election for class president. Instead of just voting for one candidate, the students needed to rank all the candidates according to preference. The table presents the results.
RANKINGS
Anton
2
3
1
3
4
2
Maria
4
1
3
4
1
3
Shelly
1
2
2
2
3
4
Troy
3
4
4
1
2
1
Number of Votes
36
53
41
27
31
45
1. Who is the winner by plurality? 2. What is the majority number of votes?
Mr. Abdul Rheman's class held an election for class president. Instead of just voting for one candidate, students need to rank all the
candidates according to their preference. The results are shown below:
Rankings
2
1
2
3
1
Y
2
1
2
3
1
3
1
3
1
2
2
Number of
8
7
7
8
6.
7
Students
Number of Votes for the Winner by Plurality.
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...
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
- 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; Yesarrow_forwardYour Question: Number of voters 21 21 10 34 38 16 1st choice C D B A C A 2nd choice B A C B A D 3rd choice A B A D B B 4th choice D C D C D C Find the winner of the election using the Pairwise Comparison method. For each comparison, enter the number of times each candidate was preferred to the other.A vs. BVotes where A is preferred to B : Votes where B is preferred to A : A vs. CVotes where A is preferred to C : Votes where C is preferred to A : A vs. DVotes where A is preferred to D : Votes where D is preferred to A : B vs. CVotes where B is preferred to C : Votes where C is preferred to B : B vs. DVotes where B is preferred to D : Votes where D is preferred to B : C vs. DVotes where C is preferred to D : Votes where D is preferred to C : Tally the results:Points for A: Points for B: Points for C: Points for D: Who is the winner? A B C D There is a tiearrow_forwardA journalist reviewing various cellular phone services surveyed 200 customers and asked each one to rank four service providers in order of preference. The group’s results are shown below. RANKINGS Red and White 3 4 2 3 4 Sprint PCS 1 1 4 4 3 Cingular 2 2 1 2 1 Nextel 4 3 3 1 2 No. of Votes 18 38 42 63 39 Using plurality with elimination, which provider is the favorite of these customers?arrow_forward
- The Science club is selecting its representative for a competition. The members rank the 4 candidates given in the preference table below: Votes 2 1 8 4 1st Berlin Anton Dianne Charles 2nd Charles Berlin Charles Berlin 3rd Dianne Charles Anton Dianne 4th Anton Dianne Berlin Anton Who is the Borda count winner? Group of answer choices Dianne Anton Berlin Charlesarrow_forwardThe librarian at a public library wants to determine what proportion of the library users are children. The librarianhas a tally sheet on which she marks whether books are checked out by an adult or a child. She records this datafor every fourth patron who checks out books.e. A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate,the party’s polling staff calls 1,200 randomly selected phone numbers. If a registered voter answers the phone oris available to come to the phone, that registered voter is asked whom he or she intends to vote for and whetherthe debate changed his or her opinion of the candidates.arrow_forwardAn election is held to choose the chair of a department at a university. The candidates are Professors Argand, Brandt, Chavez, Dietz, and Epstein (A, B, C, D, and E for short). The following table gives the preference schedule for the election. Use the table to complete parts (a) through (c). Number of Voters 4 3 6. 3 4 1st choice B B A A 2nd choice A C D A D 3rd choice 4th choice D A D B. B. E B B 5th choice E A D E (a) How many people voted in this election? voters (Type a whole number.) (b) How many first-place votes are needed for a majority? The smallest number for a majority is votes. (e) Which candidate had the fewest last-place votes? B. Aarrow_forward
- The theater society members are voting for the kind of play they will perform next semester; a comedy (C), a drama (D), or a musical (M). Their votes are summarized in the following preference table. Which type of play is selected using the pairwise comparison method? Number of Votes 14 10 10 8 1 1 First Choice M DC D M Second Choice C M C M D Third Choice DD M M C drama musical comedy Tie between musical and dramaarrow_forwardA survey was conducted to determine who was the best bad guy in the Star Wars franchise: Darth Vader, Emperor Palpatine, of General Grievous. The rankings are shown in the preference table below. Use pairwise comparison to determine who was the best bad guy among the three candidates. Rankings 1st 2nd 3rd Total Votes General Grievous O Emperor Palpatine Darth Vader Vader Palpatine Grievous 206 It was a three-way tie Palpatine Grievous Vader 415 Grievous Vader Palpatine 124arrow_forwardRaph has gone missing, and his brothers are arguing about who should go and find him. They agree to send whomever their Instagram followers choose in a poll, using the Borda Count Method. The preference table of the poll results is given below. Number of Votes 30 18 15 19 13 1st Choice Leo Donnie Leo Mikey Leo Mikey Donnie Donnie Donnie 2nd Choice 3rd Choice Mikey Donnie Mikey Leo Mikey Donnie Leo Leo Mikey Who will be sent to find Raph? Type your work and your answer below. Make sure to be detailed with your work. For the toolhar prorrarrow_forward
- please explain and show workarrow_forwardConsider the scenario of three candidates, A, B, and C, who are running for president of the student council. Determine the winner using the pairwise comparison method. Number of Votes 50 65 60 First Choice A C C Second Choice A Third Choice C B The winner isarrow_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
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
12. Searching and Sorting; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=6LOwPhPDwVc;License: Standard YouTube License, CC-BY
Algorithms and Data Structures - Full Course for Beginners from Treehouse; Author: freeCodeCamp.org;https://www.youtube.com/watch?v=8hly31xKli0;License: Standard Youtube License