Monotonicity Criterion and Plurality with Elimination A school board is going to hire a company to paint 10 of their schools over the summer. The three companies are: • Paint by Numbers (N), • Painter's Paradise (P), and • Paint by Us (U). Below are the results of the first vote. Determine if the plurality with elimination method violates the monotonicity criterion. Number of Votes 10 4 12 First N P N U Second U U P N Third U N 1. What is the majority needed to win the contract? 2. Use the plurality with elimination method to determine the winner. The company that gets eliminated is What does the chart look like now? Fill in the chart below. Number of Votes 8 10 4 12 First Second 3. Is there a winner? If so, who won. The board has some discussions about the background of the companies, and they decide to take a second vote. This time 4 people that voted N, U, P change their vote to U, N, P. 4. What does the chart look like now? Fill in the missing column. Number of Votes 8 10 First N Second P U Third U N 5. Use the plurality with elimination method to determine the winner. The company that gets eliminated is What does the chart look like now after the person gets removed? Fill in the new chart. Number of Votes 8 10 First Second 6. Who is the winner? 7. Is the monotonicity criterion violated? Explain why. Write your response below:
Monotonicity Criterion and Plurality with Elimination A school board is going to hire a company to paint 10 of their schools over the summer. The three companies are: • Paint by Numbers (N), • Painter's Paradise (P), and • Paint by Us (U). Below are the results of the first vote. Determine if the plurality with elimination method violates the monotonicity criterion. Number of Votes 10 4 12 First N P N U Second U U P N Third U N 1. What is the majority needed to win the contract? 2. Use the plurality with elimination method to determine the winner. The company that gets eliminated is What does the chart look like now? Fill in the chart below. Number of Votes 8 10 4 12 First Second 3. Is there a winner? If so, who won. The board has some discussions about the background of the companies, and they decide to take a second vote. This time 4 people that voted N, U, P change their vote to U, N, P. 4. What does the chart look like now? Fill in the missing column. Number of Votes 8 10 First N Second P U Third U N 5. Use the plurality with elimination method to determine the winner. The company that gets eliminated is What does the chart look like now after the person gets removed? Fill in the new chart. Number of Votes 8 10 First Second 6. Who is the winner? 7. Is the monotonicity criterion violated? Explain why. Write your response below:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Monotonicity Criterion and Plurality with Elimination
A school board is going to hire a company to paint 10 of their schools over the summer. The
three companies are:
• Paint by Numbers (N),
• Painter's Paradise (P), and
• Paint by Us (U).
Below are the results of the first vote. Determine if the plurality with elimination method
violates the monotonicity criterion.
Number of Votes
8
10
4
12
First
N
P
N
U
Second
P
U
U
N
Third
U
1. What is the majority needed to win the contract?
N
P
P
2. Use the plurality with elimination method to determine the winner.
The company that gets eliminated is
What does the chart look like now? Fill in the chart below.
Number of Votes
8
10
4
12
First
Second
3. Is there a winner? If so, who won.
The board has some discussions about the background of the companies, and they decide to
take a second vote. This time 4 people that voted N, U, P change their vote to U, N, P.
4. What does the chart look like now? Fill in the missing column.
Number of Votes
8
10
First
N
P
Second
P
U
Third
U
N
5. Use the plurality with elimination method to determine the winner.
The company that gets eliminated is
What does the chart look like now after the person gets removed? Fill in the new chart.
Number of Votes
8
10
First
Second
6. Who is the winner?
7. Is the monotonicity criterion violated? Explain why.
Write your response below:
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