Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Question
Chapter 4, Problem 14RE
To determine
Use the plurality with elimination method to determine the winner of the election.
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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.
Find the percentage and use the plurality method to determine the winner and explain why you chose that specific candidate.
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.
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
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
Chapter 4 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Prob. 3EECh. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Explain how to calculate the standard divisor of...Ch. 4.1 - Teacher Aides A total of 25 teacher aides are to...Ch. 4.1 - In the Hamilton apportionment method, explain how...Ch. 4.1 - Prob. 4ESCh. 4.1 - Governing Boards The following table shows how the...Ch. 4.1 - Forest Rangers The table below shows how the...
Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. What is the Balinski-Young Impossibility...Ch. 4.1 - Apportionment of Projectors Consider the...Ch. 4.1 - Hotel Management A company operates four resorts....Ch. 4.1 - Prob. 18ESCh. 4.1 - Management Scientific Research Corporation has...Ch. 4.1 - Prob. 20ESCh. 4.1 - Elementary School Teachers The following table...Ch. 4.1 - Social Workers The following table shows the...Ch. 4.1 - Computer Usage The table below shows the number of...Ch. 4.1 - The population of Illinois increased by over...Ch. 4.1 - Prob. 25ESCh. 4.1 - Prob. 26ESCh. 4.1 - Computer Usage Use the Webster method to apportion...Ch. 4.1 - Demographics The table below shows the populations...Ch. 4.1 - Which of she following apportionment methods can...Ch. 4.1 - According to Michael Balinski and H. Peyton Young,...Ch. 4.1 - 31. What method is presently used to apportion the...Ch. 4.1 - Prob. 32ESCh. 4.1 - John Quincy Adams, the sixth president of the...Ch. 4.1 - In the Huntington-Hill method of apportionment,...Ch. 4.1 - Prob. 35ESCh. 4.2 - Using the Borda method of voting, which flavor of...Ch. 4.2 - Instead of using the normal Borda method, suppose...Ch. 4.2 - Prob. 3EECh. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Prob. 5EECh. 4.2 - Can the assignment of points for first. Second,...Ch. 4.2 - Prob. 7EECh. 4.2 - Prob. 1ESCh. 4.2 - Explain why the plurality voting system may not be...Ch. 4.2 - Prob. 3ESCh. 4.2 - Explain how the plurality with elimination voting...Ch. 4.2 - Prob. 5ESCh. 4.2 - Prob. 6ESCh. 4.2 - Is there a best voting method? Is one method more...Ch. 4.2 - Explain why. if only two candidates are running,...Ch. 4.2 - Presidential Election The table below shows the...Ch. 4.2 - Breakfast Cereal Sixteen people were asked to rank...Ch. 4.2 - Cartoon Characters A kindergarten class was...Ch. 4.2 - Catering A 15-person committee is having lunch...Ch. 4.2 - Movies Fifty consumers were surveyed about their...Ch. 4.2 - Breakfast Cereal Use the Borda count method of...Ch. 4.2 - Prob. 15ESCh. 4.2 - Catering Use the Borda count method of voting to...Ch. 4.2 - Class Election A senior high school class held an...Ch. 4.2 - Cell Phone Usage A journalist reviewing various...Ch. 4.2 - Baseball Uniforms A Little League baseball team...Ch. 4.2 - Radio Stations A number of college students were...Ch. 4.2 - Class Election Use plurality with elimination to...Ch. 4.2 - Prob. 22ESCh. 4.2 - Campus Club A campus club has money left over in...Ch. 4.2 - Recreation A company is planning its annual summer...Ch. 4.2 - X-Men Movies Fans of the X-Men movies have been...Ch. 4.2 - Prob. 26ESCh. 4.2 - School Mascot A new college needs to pick a moscot...Ch. 4.2 - Election Five candidates are running for president...Ch. 4.2 - Prob. 29ESCh. 4.2 - Radio Stations Use the pairwise comparison method...Ch. 4.2 - Does the winner in Exercise tic satisfy the...Ch. 4.2 - 32. Does the winner in Exercise 12 satisfy the...Ch. 4.2 - Prob. 33ESCh. 4.2 - Prob. 34ESCh. 4.2 - Prob. 35ESCh. 4.2 - Prob. 36ESCh. 4.2 - Election Three candidates are running for mayor. A...Ch. 4.2 - Film Competition Three films have been selected as...Ch. 4.2 - 39. Election A campus club needs to elect four...Ch. 4.2 - Scholarship Awards The members of a scholarship...Ch. 4.2 - Another method of voting is to assign a weight. or...Ch. 4.2 - Prob. 42ESCh. 4.2 - Prob. 43ESCh. 4.3 - Using the data in Example 1 on page 211, list all...Ch. 4.3 - For the data in Example I on page 211, calculate...Ch. 4.3 - Prob. 3EECh. 4.3 - Prob. 4EECh. 4.3 - Create a voting system with three members that is...Ch. 4.3 - Prob. 6EECh. 4.3 - Prob. 7EECh. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - Prob. 3ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 8ESCh. 4.3 - Prob. 9ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 13ESCh. 4.3 - Prob. 14ESCh. 4.3 - Music Education A music department Consists of a...Ch. 4.3 - Prob. 16ESCh. 4.3 - Criminal Justice In a criminal trial, each of the...Ch. 4.3 - Criminal Justice In California civil court cases,...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Prob. 21ESCh. 4.3 - Prob. 22ESCh. 4.3 - Football At the beginning of each football season,...Ch. 4.3 - Prob. 24ESCh. 4.3 - Prob. 25ESCh. 4.3 - Prob. 26ESCh. 4.3 - Consider the weighted voting system { q:8,3,3,2 },...Ch. 4.3 - Prob. 28ESCh. 4.3 - Prob. 29ESCh. 4.3 - UN Security Council The United Nations C Security...Ch. 4 - Education The following table shows the...Ch. 4 - Airline Industry The following table shows the...Ch. 4 - Airline Industry The table below shows how the...Ch. 4 - 4. Education The following table shows the number...Ch. 4 - Technology A company has four offices. The...Ch. 4 - Automobile Sales Consider the apportionment of 27...Ch. 4 - Music Company MusicGalore.biz has offices in Los...Ch. 4 - Building Inspectors A city apportions 34 building...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Corporate Security The Huntington-Hill...Ch. 4 - Essay Contest Four finalists are competing in an...Ch. 4 - Ski Club A campus ski club is trying o decide...Ch. 4 - Prob. 14RECh. 4 - Consumer Preferences A group of consumers were...Ch. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Homecoming Queen Three high school students are...Ch. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - A weighted voting system for voters A. B. C. D....Ch. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - 25. Calculate the Banzhaf power indices for voters...Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - Prob. 27RECh. 4 - Identify any dictator and all dummies for each...Ch. 4 - Four voters. A. B. C. and D. make decisions by...Ch. 4 - Postal Service The table below shows the number of...Ch. 4 - Computer Allocation The following table shows the...Ch. 4 - High School Counselors The following table shows...Ch. 4 - Prob. 4TCh. 4 - Consumer Preference One hundred consumers ranked...Ch. 4 - Prob. 6TCh. 4 - Exam Review A professor is preparing an extra...Ch. 4 - Prob. 8TCh. 4 - Drama Department The four staff members. A, B,C,...Ch. 4 - Three voters. A. B. and C, make decisions by using...
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- Four candidates: Rhea , Charles ,John , and Wilson arerunning four Councilor. After the polls close, votes aretallied and the following results are obtained:Candidate and Number of votes:Rhea - 2,567 Charles - 2,445 John - 5,100 Wilson - 2,365b. How many votes were castsc. Using plurality method of voting which candidate wins?d. Did the winner receive a majority of the votes?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 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 630arrow_forwardMr. 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 2 1 Y 1 1 1 3 3 1 2 2 Number of 7 8 6 Students Winner by Plurality.arrow_forward
- Consider the scenario of three candidates, A, B, and C, who are running for president of the student council. Determine the winner using the Borda count method. Number of Votes 50 65 60 First Choice ACC Second Choice BBA Third Choice CAB The winner is The winner received points.arrow_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_forwardConsider the scenario of three candidates, A, B, and C, who are running for president of the student council. Determine the winner using the Borda count method. Number of Votes 50 65 60 First Choice AC C Second Choice BBA Third Choice CAB The winner is The winner received points.arrow_forward
- Use the plurality with elimination 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. Clubs 1 3 4 Number of Votes 19 15 11 7 2 First A В C Second В D A D Third C A A Fourth D C В В a A b C d OBA O O O Oarrow_forwardDetermine the winner using the following methods: Plurality withElimination, Borda Count and Pairwise Comparison. SHOW COMPLETE SOLUTIONarrow_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_forward
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