Exam3 - [4 WEIGHTED VOTING SYSTEMS 4.1 Describe Weighted...

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Unformatted text preview: [4] WEIGHTED VOTING SYSTEMS 4.1) Describe Weighted Voting Systems, WVS. (players, voter’s weight, quota) WVS = a system in which different voters control (or are allowed different numbers of votes. Turns out that not always a voter with more votes has more voting power than another voter with a smaller number of votes. Ex: for a resolution to pass it is necessary that 1mil +1 votes are collected. If there are 2 voters in the system (millionth vote and million+1) then the millionth voter alone cannot pass because they have the same power. Voters in the system = players. Resolutions (motions) pass if total # of votes are >/= to pre- determined quota q . Quota = minimum needed for a vote to pass. # of votes = a player’s weight. Symbol for weight = w The systems consist of 2 alternatives (yes/no) (pro/con) 4.2) Describe the notation of WVS. Mathematical rep of WVS is [ q: w1,w2,w3… wm ] Examples: [4.2.1] The system [6: 4, 3, 1] voter 1 = 4 votes, 2 = 3 votes = 3 = 1vote Pass if 6 or more are in favor. [4.2.2] The system [8: 3, 1, 1, 1, 1, 1, 1] [4.2.3] Suppose that a small corporation consists of five stockholders. Nancy (the largest stockholder) has 20 votes, Sy has 15 votes, Amal has 10 votes, Tyler has 8 votes, and Angela has 3 votes. The five members decide to form a Board of Directors to oversee the company and agree that it takes 30 or more votes to pass a motion. Represent this voting system mathematically. [16: 10,10,5,5] [4.2.4] Four brothers and sisters (two sisters and two brothers) are the owners of a trust fund. Their parents assigned ten votes to each of the two sisters and five votes to each of the two brothers. The quota for passing a measure is 16 or more votes. Represent this voting system mathematically. [4.2.5] Describe the system [63: 60, 65] SOLUTION: The system [63: 60, 65] is described as a weighted voting system with quota 63 and two voters, one holding a weight of 60 votes and the other holding a weight of 65 votes. A resolution passes whenever the total number of votes of all voters who favor the resolution is 63 or more. [4.2.6] Describe the system [37: 20, 18, 14, 12, 8] SOLUTION The system [37: 20, 18, 14, 12, 8] is described as a weighted voting system with quota 37 and five voters having voting weights 8, 12, 14, 18, and 20, respectively. A resolution passes if the total number of votes of all voters who favor the resolution is 37 or more. 4.3) Describe Restrictions on the Quota q . Examples: 4.3.1) What’s wrong with the system [2: 1, 3, 5]? 4.3.2) What’s wrong with the system [10:1,3,5] ? 4.3.3) Find the range of values of the quota q in the weighted voting system represented by [ q : 6, 4, 3, 1]....
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This note was uploaded on 03/08/2011 for the course ECO 3201 taught by Professor Smith during the Spring '11 term at FIU.

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Exam3 - [4 WEIGHTED VOTING SYSTEMS 4.1 Describe Weighted...

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