Concept explainers
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
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?
Chapter 1 Solutions
MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
Additional Math Textbook Solutions
A Survey of Mathematics with Applications (10th Edition) - Standalone book
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
Calculus Volume 2
Basic College Mathematics
- 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.arrow_forwardThis 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_forward
- Last year at a certain high school, 11 students sought the nomination for president of the student body. In how many ways could the voters (student body) rank their first 4 choices?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_forwardCompare 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_forward
- F959 - 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_forwardAnswer numbers 2-4arrow_forward
- If 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_forwardIn a group election the top 3 are given position. If there were 8 candidates how many possible options could be given for the position of President, Vice President, and Information Officer.arrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete 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