Concept explainers
a.
To find:
The majority of the candidate using the following condition,
Molina | 2, 543 |
Sobieski | 1, 532 |
Wilson | 892 |
Gambone | 473 |
Answer to Problem 1CT
Solution:
No, there is no candidate earns majority.
Explanation of Solution
Consider four candidates running for town council receive votes as follows:
Molina | 2, 543 |
Sobieski | 1, 532 |
Wilson | 892 |
Gambone | 473 |
Definition:
If n is even then the majority of voter is
If n is odd then the majority of voters is
Where n is the number of votes.
Approach:
From the given table the value of
Therefore, the majority of voters is given below,
Therefore, there is no voter pass this majority rule. Since no voter has greater than majority value.
So, there is no candidate earns majority.
b.
To find:
The winner of the election by using the plurality method.
Answer to Problem 1CT
Solution:
The winner of the election is Molina.
Explanation of Solution
Consider four candidates running for town council receive votes as follows:
Molina | 2, 543 |
Sobieski | 1, 532 |
Wilson | 892 |
Gambone | 473 |
Definition:
The Plurality Method:
Each person votes for his or her favorite candidate. The candidate receiving the most votes is declared the winner.
Approach:
From the above table the candidate Molina has most votes. So he is declared as the winner.
So, the winner of the election is Molina.
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Chapter 11 Solutions
Mathematics All Around
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