Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 15.1, Problem 16E
Applying Four Voting Methods to a Voter Profile For each of Exercises 11-18, determine the election winner using the
(a) plurality method
(b) pairwise comparison method
(c) Borda method
(d) Hare method.
In Exercises 11 and 12, a 13-member committee is selecting a chairperson. The 3 candidates are
Amy a, Byron b, and Cory c.
Each committee member completely ranked the candidates on a separate ballot. Determine the selected chairperson.
| Number of Voters | Ranking |
| 3 | e > h > g > j |
| 6 | h>e>g>j |
| 5 | j > g > e > h |
| 4 | g > e > h > j |
| 3 | j>e>h>g |
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A campus club needs to elect four officers: a president, a vice president, a secretary, and a treasurer. The club has five volunteers. Rather than vote individually for each position, the club
members will rank the candidates in order of preference. The votes will then be tallied using the Borda Count method. The candidate receiving the highest number of points will be
president, the candidate receiving the next highest number of points is vice president, the candidate receiving the next highest number of points is secretary, and the candidate receiving
the next highest number of points will be treasurer.
Rankings
Cynthia
4
2
3
Andrew
3
1
4
Jen
5
1
Hector
1
1
4
Medin
3
4
Number of votes:
24
8
15
14
For the preference schedule shown, determine who wins each position in the club.
A campus club needs to elect four officers: a president, a vice president, a secretary, and a treasurer. The club has five volunteers. Rather
than vote individually for each position, the club members will rank the candidates in order of preference. The votes will then be tallied using
the Borda Count method. The candidate receiving the highest number of points will be president, the candidate receiving the next highest
number of points is vice president, the candidate receiving the next highest number of points is secretary, and the candidate receiving the
next highest number of points will be treasurer.
Rankings
Cynthia
4
2
3
Andrew
1
4
5
Jen
1
2
3
2
Hector
1
4
1
4
Medin
3
4
5
Number of votes:
27
8
21
25
22
For the preference schedule shown, determine who wins each position in the club.
president
---Select--- ♥
vice president
---Select--- V
secretary
---Select--- v
treasurer
---Select--- v
A campus club needs to elect four officers: a president, a vice president, a secretary, and a treasurer. The club has five volunteers. Rather than vote individually for each position, the club members will rank the candidates in order of preference. The votes will then be tallied using the Borda Count method. The candidate receiving the highest number of points will be president, the candidate receiving the next highest number of points is vice president, the candidate receiving the next highest number of points is secretary, and the candidate receiving the next highest number of points will be treasurer.
Rankings
Cynthia
4
2
5
2
3
Andrew
2
3
1
4
5
Jen
5
1
2
3
2
Hector
1
5
4
1
4
Medin
3
4
3
5
1
Number of votes:
9
12
25
24
23
For the preference schedule shown, determine who wins each position in the club.
president
vice president
secretary
treasurer
Chapter 15 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by Alternative Methods For...Ch. 15.1 - Choosing a Poster Dog by Alternative MethodsFor...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...
Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Holding a Runoff Election One common solution to...Ch. 15.1 - Prob. 20ECh. 15.1 - Prob. 21ECh. 15.1 - Prob. 22ECh. 15.1 - Prob. 23ECh. 15.1 - Prob. 24ECh. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - The Pairwise Comparison Method Each table...Ch. 15.1 - Prob. 29ECh. 15.1 - Prob. 30ECh. 15.1 - The Borda Method Each table represents a Borda...Ch. 15.1 - Prob. 32ECh. 15.1 - Prob. 33ECh. 15.1 - Prob. 34ECh. 15.1 - Prob. 35ECh. 15.1 - Prob. 36ECh. 15.1 - The Coombs Method The Coombs method of voting is a...Ch. 15.1 - Prob. 38ECh. 15.1 - Prob. 39ECh. 15.1 - Prob. 40ECh. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Condorcet...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Prob. 9ECh. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.2 - Prob. 18ECh. 15.2 - Prob. 19ECh. 15.2 - Irrelevant Alternatives in a Hare Method Election...Ch. 15.2 - 21. Explain why a violation of the majority...Ch. 15.2 - Prob. 22ECh. 15.2 - Prob. 23ECh. 15.2 - Prob. 24ECh. 15.2 - Prob. 25ECh. 15.2 - Prob. 26ECh. 15.2 - Prob. 27ECh. 15.2 - Prob. 28ECh. 15.2 - Prob. 29ECh. 15.2 - Prob. 30ECh. 15.2 - Prob. 31ECh. 15.2 - Prob. 32ECh. 15.2 - Prob. 33ECh. 15.2 - Prob. 34ECh. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Solve each problem.
5. New Trees for Wisconsin...Ch. 15.3 - Apportioning Computers to Schools Enrollments for...Ch. 15.3 - Assigning Faculty to Courses The English...Ch. 15.3 - 8. Apportioning Sailboats to Resorts The number of...Ch. 15.3 - Prob. 9ECh. 15.3 - 10. Show that the Webster method apportionment of...Ch. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Find the Huntington-Hill cutoff point for rounding...Ch. 15.3 - Creating a Profile of School Bus Riders Create a...Ch. 15.3 - Prob. 18ECh. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - The standard quotas rounded up to the nearest...Ch. 15.3 - Prob. 22ECh. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Prob. 20ECh. 15.4 - Prob. 21ECh. 15.4 - Prob. 22ECh. 15.4 - Prob. 23ECh. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - 26. The Jefferson and Adams methods are both...Ch. 15 - How many different complete rankings are possible...Ch. 15 - Prob. 2TCh. 15 - Prob. 3TCh. 15 - Prob. 4TCh. 15 - Prob. 5TCh. 15 - Why is the irrelevant alternatives criterion an...Ch. 15 - Prob. 7TCh. 15 - Prob. 8TCh. 15 - Prob. 9TCh. 15 - Prob. 10TCh. 15 - Prob. 11TCh. 15 - Prob. 12TCh. 15 - Prob. 13TCh. 15 - Prob. 14TCh. 15 - Prob. 15TCh. 15 - Prob. 16TCh. 15 - Prob. 17TCh. 15 - Prob. 18TCh. 15 - Prob. 19TCh. 15 - Prob. 20TCh. 15 - Prob. 21TCh. 15 - Prob. 22TCh. 15 - Prob. 23TCh. 15 - Prob. 24TCh. 15 - Prob. 25TCh. 15 - One hundred seats are to be apportioned to 4...Ch. 15 - Prob. 27TCh. 15 - Prob. 28TCh. 15 - Prob. 29TCh. 15 - Explain the Alabama paradox.Ch. 15 - Prob. 31TCh. 15 - Prob. 32T
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
- Choosing Officers From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer need to be filled. In how many different ways can the offices be filled?arrow_forwardConsider 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?arrow_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
- A chamber of commerce election has 18 candidates for 7 positions. The election consists of two stages. In the first stage, there is an ordered election, with the president being selected first, followed by the vice-president, and then the treasurer, and finally the secretary. In the second stage, the remaining seats are considered 'at large' seats. All the remaining candidates are considered and the 'at large' seats are selected at the same time. How many possible board combinations are there? 1,113,840 margin of error +/- 2.5%arrow_forwardThe members of a club are going to elect a president from four nominees using the Borda count method. The 30 members of the club mark their ballots as shown in the table below, where each first-place vote receives 4 points, each second-place vote receives 3 points, each third- place votes receives 2 points, and the last-place vote receives 1 point. Rankings LITI Brenda 4 1 3 2 KD 2 3 4 1 4 Alexa 3 2 2 1 Anji 1 4 3 4 Number of Voters 10 6 6 5 3 Then, the total points obtained by Brenda is the total points obtained by KD is the total points obtained by Alexa is the total points obtained by Anji is By Borda count method, is elected president.arrow_forwardDetermine whether any of the listed candidates has a majority. Four candidates running for mayor receive votes as follows. Ito: 40,761 Johnson 18,116 Kennedy:9,058 Lieberman 13,587arrow_forward
- Out of 333 Institutions, only 45% have participated in a survey. Furthermore, one person did the survey for each of the participating institutions. 8 categories were provided in the survey that participants could select. In total, the survey counted 450,5 votes. Question: How many of these categories were participants required to select when completing the survey?arrow_forwardThe Rosetown community association plans to meet once each month. The association members are deciding what day of the week to meet by holding a vote. The choices are Monday (M), Tuesday (T), and Friday (F). Instead of voting for only one day, each member ranks the three days in order of preference. Each member's ballot gives the member's first, second, and third choice for a monthly meeting day. Here are the ballots submitted. Baliot 1 Ballot 2 Ballot 3 Ballot 4 Ballot 5 Ballot 6 Balot 7 Ballot 8 Ballot 9 1st M. 14 M F. M. 1st 2n 2n 2nd 2nd M M T. 2nd 2 2nd 2nd 2nd M. 3rd 3rd 3rd F 3rd 3rd M 3rd 3rd M. 3rd Ballot 10 Ballot 11 Ballot 12 Ballot 13 Balot 14 Ballot 15 Ballot 16 1st F M 1st T. M 14 2nd T. 2nd T. 2nd 2ne 20 2n M 2nd F M 3rd M 3rd 3rd M 3rd 3 3rd Construct a preference table to summarize the ballots. You can add or remove columns in the table as needed. Note: The individual ballots above will highlight when clicked. (Highlighting the ballots can help you with your…arrow_forwardA. How many voters are there?B. How many voters have ranked the candidates in the order C, B, A, D?C. What is the minimum number of voters needed to form a majority?D. Who is the winner using the Plurality Voting method?E. Find the points each candidate received using the basic Borda Count method.A = ____ points; B = ____ points; C = ____ points; D = ____ points.F. Who is the winner using the Hare system?G. Find the points each candidate received using the Pairwise Comparisonmethod.A = ____ points; B = ____ points; C = ____ points; D = ____ points.arrow_forward
- A company has four divisions with 560, 1230, 1490, and 1760 people, respectively. A total of 18 IT workers must be allocated to each division according to their size. Complete parts (a) through (d) to find the apportionment using the Hill-Huntington method. Find the standard divisor. Find the standard quota and modified standard quota for each division. Using a modified standard divisor of 275, find the modified quota for each division. Find the geometric mean for each division. Show the rounded quota (according to the Hill-Huntington method) for each division and the final apportionment of IT workers. PLEASE WATCH GRAMMAR, PUNCTUATION, AND HAVE CLEAR FORMATTING. Thank you.arrow_forwardfive candidates: claire, jimmy, jessie, kent and gina are running for president of the student government. after the polls close, votes are called and the results in the table below are obtained: candidate claire jimmy jessie number of 318 402 760 votes questions: a. how many votes were casted? b. using the plurality method of voting, which candidate wins? c. did the winner receive majority of the votes? kent gina 1,035 485arrow_forwardWhat is a weighted voting system?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
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