Chapter 14, Problem 1RE

Electing the Club President The Sailing Club of Lakeport is holding an election to choose the club president. The 42 votes were cast as follows: Comstock, 20 votes, Owens, 15 votes, and Glazer, 7 votes.

1. a. Using the plurality method, which candidate is elected president?
2. b. Did this candidate receive a majority of votes?

To determine

To find: The candidate who is elected as a president by using the plurality method.

Answer to Problem 1RE

The Comstock wins the election with most votes 20.

Explanation of Solution

Given:

The sailing club of Lakeport is holding an election to choose the club. The 42 votes were cast as follows: Comstock, 20 votes; Owens, 15 votes; and Glazer, 7 votes.

Voting method used:

Plurality voting method:

1. Each voter votes for one candidate.

2. The candidate receiving the most votes is declared the winner.

Calculation:

From the given, it is noticed that the votes received by the three candidates are 20, 15 and 7.

Among three the Comstock receives the most number of votes as compare to other two candidates

By the plurality method, the Comstock wins the president election with most number of 20 votes.

Therefore, the Comstock wins the election with most number of votes as 20.

To determine

To Check: Whether the Comstock receives the majority of votes or not.

Answer to Problem 1RE

The Comstock received only 20 votes which is not a majority of votes.

Explanation of Solution

Given that the total number of votes is 42.

Then the candidate to acquire a majority of votes they should receive a majority of 22 or more number of votes.

It is known that the majority out of 42 votes is 22 or more votes.

But Comstock received only 20 votes which is not the majority of votes out of 42 votes.

That is, it is clear that the candidate does not reach the vote 22.

Therefore, it is concluded that the Comstock received only 20 votes which is not a majority of votes.