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103s11chap2Asolutions

# 103s11chap2Asolutions - Math 103 Spring 2010 Solutions to...

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Math 103, Spring 2010, Solutions to Chapter 2A homework 16 points total Problem 18 b: 4 points The weighted voting system [17:16, 8, 4, 1] has the following winning coalitions, with the critical player(s) in each winning coalition underlined: {P 1 , P 2 , P 3 , P 4 } {P 1 , P 2 , P 3 } { P 1 , P 2 , P 4 } { P 1 , P 3 , P 4 } { P 1 , P 2 } { P 1 , P 3 } { P 1 , P 4 } The Banzhaf power distribution for this weighted voting system is as follows: P 1 has 7/10 = 70% of the power P 2 has 1/10 = 10% of the power P 3 has 1/10 = 10% of the power P 4 has 1/10 = 10% of the power Remark: P 1 belongs to every winning coalition, and therefore has veto power. P 4 has some share in the real power, and is therefore not a dummy. In spite of the fact that P 2 has twice the weight of P 3 and eight times the weight of P 4 , they have all have the same fraction of the real power as measured by Banzhaf's approach. __________________________________________________________________ Problem 18c: 4 points The weighted voting system [18:16, 8, 4, 1] has the following winning coalitions, with the critical player(s) in each winning coalition underlined: {P 1 , P 2 , P 3 , P 4 } {P 1 , P 2 , P 3 } { P 1 , P 2

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103s11chap2Asolutions - Math 103 Spring 2010 Solutions to...

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