Weighted Voting

Weighted Voting Systems © 2010 Pearson Education, Inc. All rights reserved. Section 12.3, Slide 2

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 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. © 2010 Pearson Education, Inc. All rights reserved. Section 12.3, Slide 4

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

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

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

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

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 9

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

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

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

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 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. © 2010 Pearson Education, Inc. All rights reserved. Section 12.3, Slide 14

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. © 2010 Pearson Education, Inc. All rights reserved. Section 12.3, Slide 15

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. © 2010 Pearson Education, Inc. All rights reserved. Section 12.3, Slide 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. © 2010 Pearson Education, Inc. All rights reserved. Section 12.3, Slide 17

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) © 2010 Pearson Education, Inc. All rights reserved. Section 12.3, Slide 18

Coalitions Solution: We list all possible subsets of the set {R, D, I}. © 2010 Pearson Education, Inc. All rights reserved. Section 12.3, Slide 19

Coalitions In the previous example we have: © 2010 Pearson Education, Inc. All rights reserved. Section 12.3, Slide 20