# DM.8. Is a set of numbers that are listed in the following format: [ quota: weight of voter 1, weight of voter 2,…weight of voter 3] Ex: [8:5,4,3,2]

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DM.8

Is a set of numbers that are listed in the following format: [ quota: weight of voter 1, weight of voter 2,…weight of voter 3] Ex: [8:5,4,3,2]

The quota is the number of votes necessary in this system to get a resolution passed. The number that follows, called weights, are the amount of votes controlled by voter 1, voter 2, etc.. In weighted voting if one person meets quota they are considered the dictator and everyone else are considered dummies. If there is no dictator everyone is considered to have some sort of power because they are needed to achieve quota.

The only person that has veto power is the dictator. Any set of voters who vote the same way is called a coalition. The sum of the weights of the voters in a coalition is called the weight of the coalition. If a coalition has a weight that is greater than or equal to the quota then that coalition is called a winning coalition.

[6:4,3,2,1] a) How many voters do we have? b) What is the total number of votes? c) What is the quota? d) Does anyone have a dictatorship? e) List all the winning coalitions:

[14:15,2,3,3,5] a) How many voters do we have? b) What is the total number of votes? c) What is the quota? d) Does anyone have a dictatorship? e) List all the winning coalitions:

A critical voter is someone that when he or she leaves the coalition then the coalition will no longer be a winning coalition. Example: [11:9,8,3] Critical voters R -9 D -8 I -3 RD -17 RI -12 DI - 11 RDI -20

A voters Banzhaf Power index is defined as: The number of times the voter is critical in winning coalitions divided by the total number of times voters are critical in winning coalitions From previous example: R, D and I were critical voters twice.

See handout Classwork – Pg 67-68 2,4,8,11,14 Homework – Pg 67-68 1,3,7,12,13

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