1. Voting and Apportionment
Active Learning Lecture Slides
For use with Classroom Response Systems
Chapter 15
Voting and Apportionment

2. The employees at a local law firm are voting on the entrée for their annual holiday party. Their choices are chicken (C), salmon (S), and steak (T). The preference table follows.
Number of Votes 30 18 12 23
First T C S
Second
Third

3. Here’s the preference table, again. How many employees voted?
Number of Votes 30 18 12 23
First T C S
Second
Third
a b c d. 83

4. Here’s the preference table, again. How many employees voted?
Number of Votes 30 18 12 23
First T C S
Second
Third
a b c d. 83

5. Here’s the preference table, again
Here’s the preference table, again. Does any choice have a majority of votes?
Number of Votes 30 18 12 23
First T C S
Second
Third
a. Yes. b. No. c. Can’t determine.

6. Here’s the preference table, again
Here’s the preference table, again. Does any choice have a majority of votes?
Number of Votes 30 18 12 23
First T C S
Second
Third
a. Yes. b. No. c. Can’t determine.

7. Here’s the preference table, again
Here’s the preference table, again. Determine the winner using the plurality method.
Number of Votes 30 18 12 23
First T C S
Second
Third
a. Chicken b. Salmon
c. Steak d. Can’t determine

8. Here’s the preference table, again
Here’s the preference table, again. Determine the winner using the plurality method.
Number of Votes 30 18 12 23
First T C S
Second
Third
a. Chicken b. Salmon
c. Steak d. Can’t determine

9. Here’s the preference table, again
Here’s the preference table, again. Determine the winner using the Borda count method.
Number of Votes 30 18 12 23
First T C S
Second
Third
a. Chicken b. Salmon
c. Steak d. Can’t determine

10. Here’s the preference table, again
Here’s the preference table, again. Determine the winner using the Borda count method.
Number of Votes 30 18 12 23
First T C S
Second
Third
a. Chicken b. Salmon
c. Steak d. Can’t determine

11. Here’s the preference table, again
Here’s the preference table, again. Determine the winner using the plurality method with elimination method.
Number of Votes 30 18 12 23
First T C S
Second
Third
a. Chicken b. Salmon
c. Steak d. Can’t determine

12. Here’s the preference table, again
Here’s the preference table, again. Determine the winner using the plurality method with elimination method.
Number of Votes 30 18 12 23
First T C S
Second
Third
a. Chicken b. Salmon
c. Steak d. Can’t determine

13. Here’s the preference table, again
Here’s the preference table, again. Determine the winner using the pairwise comparison method.
Number of Votes 30 18 12 23
First T C S
Second
Third
a. Chicken b. Salmon
c. Steak d. Can’t determine

14. Here’s the preference table, again
Here’s the preference table, again. Determine the winner using the pairwise comparison method.
Number of Votes 30 18 12 23
First T C S
Second
Third
a. Chicken b. Salmon
c. Steak d. Can’t determine

15. The employees also must pick the dessert for their holiday party
The employees also must pick the dessert for their holiday party. The choices are cheese cake (C), apple tart (A), chocolate mousse cake (M), or vanilla ice cream (V). Here’s the preference table.
Number of Votes 19 16 12 22 14
First A C M V
Second
Third
Fourth

16. Which dessert wins this election if the plurality method is used?
Number of Votes 19 16 12 22 14
First A C M V
Second
Third
Fourth
a. Cheese cake b. Apple tart
c. Chocolate Mousse d. Vanilla ice cream

17. Which dessert wins this election if the plurality method is used?
Number of Votes 19 16 12 22 14
First A C M V
Second
Third
Fourth
a. Cheese cake b. Apple tart
c. Chocolate Mousse d. Vanilla ice cream

18. Which dessert wins this election if the Borda count method is used?
Number of Votes 19 16 12 22 14
First A C M V
Second
Third
Fourth
a. Cheese cake b. Apple tart
c. Chocolate Mousse d. Vanilla ice cream

19. Which dessert wins this election if the Borda count method is used?
Number of Votes 19 16 12 22 14
First A C M V
Second
Third
Fourth
a. Cheese cake b. Apple tart
c. Chocolate Mousse d. Vanilla ice cream

20. Which dessert wins this election if the plurality with elimination method is used?
Number of Votes 19 16 12 22 14
First A C M V
Second
Third
Fourth
a. Cheese cake b. Apple tart
c. Chocolate Mousse d. Vanilla ice cream

21. Which dessert wins this election if the plurality with elimination method is used?
Number of Votes 19 16 12 22 14
First A C M V
Second
Third
Fourth
a. Cheese cake b. Apple tart
c. Chocolate Mousse d. Vanilla ice cream

22. Which dessert wins this election if the pairwise comparison method is used?
Number of Votes 19 16 12 22 14
First A C M V
Second
Third
Fourth
a. Cheese cake b. Apple tart
c. Chocolate Mousse d. Vanilla ice cream

23. Which dessert wins this election if the pairwise comparison method is used?
Number of Votes 19 16 12 22 14
First A C M V
Second
Third
Fourth
a. Cheese cake b. Apple tart
c. Chocolate Mousse d. Vanilla ice cream

24. Which voting method(s) – plurality, Borda count, plurality with elimination, or pairwise comparison – violate the majority criterion using the following election data?
Number of Votes 10 15 20
First A B C
Second
Third
a. Plurality b. Plurality with elimination
c. Borda count d. Pairwise comparison

25. Which voting method(s) – plurality, Borda count, plurality with elimination, or pairwise comparison – violate the majority criterion using the following election data?
Number of Votes 10 15 20
First A B C
Second
Third
a. Plurality b. Plurality with elimination
c. Borda count d. Pairwise comparison

26. The high school band is voting on a new mascot
The high school band is voting on a new mascot. Their choices are a bulldog (B), an eagle (E), and a wildcat (W). The 75 committee members rank their choices according to the following preference table. Does the plurality with elimination method violate the head- to-head criterion?
Number of Votes 23 20 17 15
First B E W
Second
Third
a. Yes b. No c. Can’t determine

27. The high school band is voting on a new mascot
The high school band is voting on a new mascot. Their choices are a bulldog (B), an eagle (E), and a wildcat (W). The 75 committee members rank their choices according to the following preference table. Does the plurality with elimination method violate the head- to-head criterion?
Number of Votes 23 20 17 15
First B E W
Second
Third
a. Yes b. No c. Can’t determine