1. Weighted Voting

2. Weighted Voting Systems
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Section 12.3, Slide 2

3. Weighted Voting Systems
Example: Explain the weighted voting system.
[51 : 26, 26, 12, 12, 12, 12]
Solution: The following diagram describes how to interpret this system.
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Section 12.3, Slide 3

4. Weighted Voting Systems
Example: Explain the weighted voting system.
[51 : 26, 26, 12, 12, 12, 12]
Solution: The following diagram describes how to interpret this system.
© 2010 Pearson Education, Inc. All rights reserved.
Section 12.3, Slide 4

5. Weighted Voting Systems
Example: Explain the weighted voting system.
[4 : 1, 1, 1, 1, 1, 1, 1]
Solution: This is an example of a “one person one vote” situation.
© 2010 Pearson Education, Inc. All rights reserved.
Section 12.3, Slide 5

6. Weighted Voting Systems
Example: Explain the weighted voting system.
[4 : 1, 1, 1, 1, 1, 1, 1]
Solution: This is an example of a “one person one vote” situation.
© 2010 Pearson Education, Inc. All rights reserved.
Section 12.3, Slide 6

7. Weighted Voting Systems
Example: Explain the weighted voting system.
[14 : 15, 2, 3, 3, 5]
Solution: Voter 1 is a dictator.
© 2010 Pearson Education, Inc. All rights reserved.
Section 12.3, Slide 7

8. Weighted Voting Systems
Example: Explain the weighted voting system.
[14 : 15, 2, 3, 3, 5]
Solution: Voter 1 is a dictator.
© 2010 Pearson Education, Inc. All rights reserved.
Section 12.3, Slide 8

9. Weighted Voting Systems
Example: Explain the weighted voting system.
[10 : 4, 3, 2, 1]
Solution: Every voter has veto power.
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Section 12.3, Slide 9

10. Weighted Voting Systems
Example: Explain the weighted voting system.
[10 : 4, 3, 2, 1]
Solution: Every voter has veto power.
© 2010 Pearson Education, Inc. All rights reserved.
Section 12.3, Slide 10

11. Weighted Voting Systems
Example: Explain the weighted voting system.
[12 : 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
Solution: Every voter has veto power. This describes our jury system.
© 2010 Pearson Education, Inc. All rights reserved.
Section 12.3, Slide 11

12. Weighted Voting Systems
Example: Explain the weighted voting system.
[12 : 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
Solution: Every voter has veto power. This describes our jury system.
© 2010 Pearson Education, Inc. All rights reserved.
Section 12.3, Slide 12

13. Weighted Voting Systems
Example: Explain the weighted voting system.
[12 : 1, 2, 3, 1, 1, 2]
Solution: The sum of all the possible votes is less than the quota, so no resolutions can be passed.
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Section 12.3, Slide 13

14. Weighted Voting Systems
Example: Explain the weighted voting system.
[12 : 1, 2, 3, 1, 1, 2]
Solution: The sum of all the possible votes is less than the quota, so no resolutions can be passed.
© 2010 Pearson Education, Inc. All rights reserved.
Section 12.3, Slide 14

15. Weighted Voting Systems
Example: Explain the weighted voting system.
[39 : 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
Solution: This system describes the voting in the UN Security Council.
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Section 12.3, Slide 15

16. Coalitions In a weighted voting system [4 : 1, 1, 1, 1, 1, 1, 1]
any coalition of four or more voters is a winning coalition.
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Section 12.3, Slide 16

17. Coalitions In a weighted voting system [4 : 1, 1, 1, 1, 1, 1, 1]
any coalition of four or more voters is a winning coalition.
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Section 12.3, Slide 17

18. Coalitions
Example: A town has three parties: (R)epublican, (D)emocrat, and (I)ndependent. Membership on the town council is proportional to the size of the parties with R having 9 members, D having 8, and I only 3. Parties vote as a single bloc, and resolutions are passed by a simple majority. List all possible coalitions and their weights, and identify the winning coalitions.
(continued on next slide)
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Section 12.3, Slide 18

19. Coalitions
Solution: We list all possible subsets of the set {R, D, I}.
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Section 12.3, Slide 19

20. Coalitions In the previous example we have:
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Section 12.3, Slide 20