1. Plurality and Borda Count Method
Voting Methods
Plurality and Borda Count Method

2. Plurality and Borda Count
T. Serino
Plurality and Borda Count
Content Objective: Students will be able to determine the winner of an election using the Plurality method and the Borda Count Method.   
Language Objective: Students will be able to distinguish between number of points received and number of votes received (1st place, 2nd place, 3rd place etc.).

3. Plurality Method
T. Serino
The Plurality Method simply says that the candidate with the most first place votes wins.
This is a popular method, but is it always reasonable?
Remember the election between these three candidates?

4. Plurality Method How does this election turn out using plurality?
T. Serino
How does this election turn out using plurality?

5. Plurality Method
T. Serino A B C B A C C B A C B A B A C C A B A B C
Making a guess on the two unknown ballots, the preference table would look like this.

6. Plurality Method
T. Serino
The result of the election by plurality method is that Carl (C) wins with 3 first place votes.
Amy: votes
Beatrice: votes
Carl: votes
Is this fair? Why is the majority unhappy?

7. Plurality Method A wins!
T. Serino
Remember the Mathematics Anxiety Club? The preference table for their election is shown below.
A = 14
B = 4
C = 11
D = 8
Tally the number of first place votes for each candidate. Who wins?
A wins!

8. Plurality Method
T. Serino
Using the plurality method, determine the winner of the election that produced the preference table below.
1st B C A D A A
2nd D B D B D C
3rd C D B C B B
4th E E E E C D
5th A A C A E E
How many votes did the winner receive?

9. Borda Count
T. Serino
Using the Borda Count method, votes are weighted according to order of preference.   
Each last place vote earns a candidate 1 point.
Each second to last place vote earns a candidate 2 points.
Each third to last place vote earns a candidate 3 points.
Etc.
If there are N candidates, first place is votes are worth N points, second place votes are worth (N-1) points, etc.

10. Weighted Voting With three candidates: With four candidates:
T. Serino
With three candidates:
Each 1st place vote is worth 3 pts.
Each 2nd place vote is worth 2 pts.
Each 3rd (last) place vote is worth 1 pt.
With four candidates:
Each 1st place vote is worth 4 pts.
Each 2nd place vote is worth 3 pts.
Each 3rd place vote is worth 2 pts.
Each 4th (last) place vote is worth 1 pt.

11. Borda Count Remember the election between these three candidates?
T. Serino
Remember the election between these three candidates?

12. Borda Count
T. Serino
Amy receives 2 first place votes worth 3 points each = 6 pts.
Amy receives 3 second place votes worth 2 pts. ea. = 6 pts.
Amy receives 2 last place votes worth 1 point each = 2 pts.
Amy earns a total of = 14 points
Use tables to organize the results for each candidate.

13. Borda Count Amy: 1st 2 x 3 = 6 2nd 3 x 2 = 6 3rd 2 x 1 = 2 14 points
T. Serino
Amy: 1st 2 x 3 = 6
2nd 3 x 2 = 6
3rd 2 x 1 = 2
14 points
Beatrice: 1st 2 x 3 = 6
2nd 4 x 2 = 8
3rd 1 x 1 = 1
15 points
Carl: 1st 3 x 3 = 9
2nd 0 x 2 = 0
3rd 4 x 1 = 4
13 points
Number
of votes.
Points
per vote.
Total points
earned.

14. Try this. By the Borda Count method, who will be
T. Serino
By the Borda Count method, who will be
the new president of the MAC?

15. Borda Count 14 56 4 16 24 72 9 18 23 23 79 points 106 points 11 44 8
T. Serino 14 56 4 16 24 72 9 18 23 23
79 points
106 points 11 44 8 32 8 24 5 15 18 36 10 20 14 14
104 points
81 points

16. athematical M D
ecision
aking