Weighted Voting Systems Chapter 2 Objective Recognize the

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.

�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. Closing Product Exit Ticket

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

Examples

�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 , . . , wn �Quota – the minimum number of votes needed to pass a motion; notated by q. Characteristics

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

50% < q ≤ 100% Quota Criteria

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 13 Example #1 6 20 4

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? Example #2

�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 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 Example #3

[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). Consider the following …. .