Question

In: Math

A group of college students want to have a party. They need to decide if they...

A group of college students want to have a party. They need to decide if they want to have it at the Beach (B) or at the Park (P) or in a Warehouse (W). They were ask to list in order their 1st, 2nd, and 3rd choice of where they want to have the party. Use the following table and answer the following questions. SHOW YOUR WORK to receive full credit.

10 students

8 students

13 students

1 st choice

W

B

P

2 nd choice

B

W

B

3 rd choice

P

P

W

a. How many votes were cast?

b. Use the plurality method to determine the winner.

c. Use the instant runoff method to determine the winner.

d. Use the Borda count method to determine the winner.

Solutions

Expert Solution

a. How many votes were cast?

Total number of votes = 10 + 8 + 13 = 31

We only about the number of students who voted. In 1 vote they have choices which does not increase the number of votes.

b. Use the plurality method to determine the winner.

The plurality method only considers about the first choice.

10 students which is the highest would like to have party at warehouse as their first choice.

Therefore according to the plurality method Warehouse is the winner.

c. Use the instant runoff method to determine the winner.

in the instant runoff method we start by listing down the winner of the first choice which will have more than 50% of the votes.

Until we get this we keep eliminating the preference having the lowest first choice. As we keep eliminating the next choice will replace its position

Out of 31 votes more than 50% means 16 votes will be the majority. Since no place has gotten 16 votes as the first choice we will start eliminating.

10 students 8 students 13 students

1 st choice

W

B

P

2 nd choice

B

W

B

3 rd choice

P

P

W

B (beach ) has gotten lowest first choice. So we will eliminate from everywhere

10 students 8 students 13 students

1 st choice

W

P

2 nd choice

W

3 rd choice

P

P

W

Replacing the next choices our new table will be

10 students 8 students 13 students

1 st choice

W

W

P

2 nd choice

P

P

W

If we look now Warehouse has 10 + 8 = 18 as the first choices which is more than majority (16)

Therefore according to the instant runoff method Warehouse is the winner.

d. Use the Borda count method to determine the winner.

In this we are going to give points to each choice going from 1 - 3 (3 being the highest). Highest points will be given to the first choice and it will decrease accordingly. These will be multiplied by their respective votes. Place with maximum count will be the winner

10 students 8 students 13 students

1 st choice

3

W

3 * 10 = 30

B

3 * 8 = 24

P

3 * 13 = 39

2 nd choice

2

B

2 * 10 = 20

W

2 * 8 = 16

B

2 * 13 = 26

3 rd choice

1

P

10

P

8

W

13

W = 30 + 16 + 13 = 59

B = 24 + 20 + 26 = 70

P = 39 + 10 + 13 = 62

Therefore according to the borda count method beach is the winner.

milcah answered 1 year ago
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