1. Weighted Voting Systems Chapter 2 Objective: Recognize the notation for weighted voting system and be able to define quota, player, dictator, dummy and veto power.

2. Closing Product Exit Ticket Analyze two different weighted voting scenarios & identify the quota and players in proper notation. In addition, identify which player(s) is the dictator, dummy and has the veto power.

3. Weighted Voting Systems Any formal voting arrangement in which voters are not necessarily equal in terms of number of votes they control.

4. Examples

5. Characteristics Players – the voters; denoted P 1, P 2, P 3,...., P n Weights - the number of votes each player controls; denoted w 1, w 2, w 3,...., w n Quota – the minimum number of votes needed to pass a motion; notated by q.

6. Weighted Voting System Notation [ q; w 1, w 2, w 3,...., w n ] Quota # of votes of P 1 Weights are written in descending order # of votes of P 2

7. Quota Criteria 50% < q ≤ 100%

8. Example #1 Consider the weighted voting system [13: 7, 4, 3, 3, 2, 1]. Find the following: a) The total number of players b) The total number of votes c) The weight of P 2 d) The minimum number of votes needed to pass a motion 20 6 4 13

9. Example #2 Consider the weighted voting system [q: 10, 6, 5, 4, 2] a) What is the smallest value that the quota q can take? b) What is the largest value that the quota q can take? c) What is the value of the quota if at least two-thirds votes is needed to pass a motion? d) What is the value of the quota if more than two-thirds of the votes are required to pass a motion?

10. Example #3 A committee has four members (P 1, P 2, P 3, and P 4 ). In this committee P 1 has twice as many votes as P 2 ; P 2 has twice as many votes as P 3 ; P 3 has twice as many votes as P 4. Describe the committee as a weighted voting system when the requirements to pass a motion are

11. Example #3 a) At least two-thirds of the votes. b) More than two-thirds of the votes. c) At least 80% of the votes. d) More than 80 % of the votes

12. Consider the following ….. [6: 7, 3, 1] Dictator – a player who’s weight is greater than the quota. Dummy – a player who has no power (influence over the outcome).

13. Consider the following …. [q:4, 2, 1] Veto Power – a player who is not the dictator has this power if a motion cannot pass without his votes.

14. Example # 4 [19: 9, 7, 5, 3, 1][15: 16, 8, 4, 1] Dictator? Dummy? Veto Power? Dictator? Dummy? Veto Power?