Chapter 11.CT, Problem 1CT

To determine

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 $\frac{n}{2}+1$

If n is odd then the majority of voters is $\frac{n+1}{2}$

Where n is the number of votes.

Approach:

From the given table the value of $n=2543+1532+892+473=5440$

Therefore, the majority of voters is given below,

$\begin{array}{rll}\frac{n}{2}+1& =& \frac{5440}{2}+1\\ & =& 2720+1\\ & =& 2721\end{array}$

Therefore, there is no voter pass this majority rule. Since no voter has greater than majority value.

So, there is no candidate earns majority.

To determine

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.