103s11chap2Bsolutions

103s11chap2Bsolutions - Math 103, Spring 2010, Solutions to...

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14 points total Problem 28d: 4 points For the weighted voting system [14: 8, 4, 2, 1], there are 4! = 24 sequential coalitions, as follows (with pivotal player underlined in each one): < P 1 , P 2 , P 3 , P 4 > < P 1 , P 2 , P 4 , P 3 > < P 1 , P 3 , P 2 , P 4 > < P 1 , P 3 , P 4 , P 2 > < P 1 , P 4 , P 2 , P 3 > < P 1 , P 4 , P 3 , P 2 > < P 2 , P 1 , P 3 , P 4 > < P 2 , P 1 , P 4 , P 3 > < P 2 , P 3 , P 1 , P 4 > < P 2 , P 3 , P 4 , P 1 > < P 2 , P 4 , P 1 , P 3 > < P 2 , P 4 , P 3 , P 1 > < P 3 , P 1 , P 2 , P 4 > < P 3 , P 1 , P 4 , P 2 > < P 3 , P 2 , P 1 , P 4 > < P 3 , P 2 , P 4 , P 1 > < P 3 , P 4 , P 1 , P 2 > < P 3 , P 4 , P 2 , P 1 > < P 4 , P 1 , P 2 , P 3 > < P 4 , P 1 , P 3 , P 2 > < P 4 , P 2 , P 1 , P 3 > < P 4 , P 2 , P 3 , P 1 > < P 4 , P 3 , P 1 , P 2 > < P 4 , P 3 , P 2 , P 1 > The Shapley-Shubik power distribution for this weighted voting system is P 1 has 8/24 = 33 1/3 % of the power P 2 has 8/24 = 33 1/3 % of the power
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103s11chap2Bsolutions - Math 103, Spring 2010, Solutions to...

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