Chapter 15.1, Problem 1E

Choosing a Poster Dog by the Plurality Method A local animal shelter is choosing a poster dog

The choices are an Australian shepherd a, a boxer b, a cocker spaniel c, or a dalmatian d. Thirteen staff members completely rank the four dogs on their ballots. The thirteen individual

ballots are the columns in the table. In each of Exercises 1 and 2, complete the following.

(a) How many different ways can a staff member complete his or her ballot?

(b) Write a voter profile for this election.

(c) Use the plurality method to determine the shelter's poster dog.

Voter

1

2

3

4

5

6

7

8

9

10

11

12

13

1st place

b

b

a

c

d

d

c

c

b

a

a

a

a

2nd place

c

c

d

d

c

a

a

a

c

c

d

b

b

3rd place

a

a

c

b

b

b

d

d

a

d

c

c

c

4th place

d

d

b

a

a

c

b

b

d

b

b

d

d