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Answer all three parts HomeWork. Section 2.3 Homework Score: 0 of 1 pt 2.3.33 5

ID: 3041949 • Letter: A

Question

Answer all three parts HomeWork. Section 2.3 Homework Score: 0 of 1 pt 2.3.33 5 of 7 (0 complete) Find the Shapley-Shubik power distribution of each of the following weighted voting systems. (a) 1111: 80, 60, 50, 20 (b) [119: 80, 60, 50, 20] (Hint: Compare this situation with the one in (a).) (c) [120: 80,60, 50, 20 (a) Find the Shapley-Shubik power distribution of (111: 80, 60, 50, 20) I.Oz Type integers or simplified fractions.) onten ia ch Succe e Option Enter your answer in the edit fields and then click Check Answer. ions Toolsremaining parts Clear All This course (MAT100-870 2018SP) is based on Tannenbaum: Excursions in Modern Mathes

Explanation / Answer

To calculate Shapley-shubik power distribution of weighted voting systems, we need to do the following 4 steps

1) List all sequential coalitions. Since there are 4 players, there are total of 4!=24 coalitions.

2) In each sequential coalition, identify the pivotal player.

For example consider the coalition <P1,P2,P3,P4>. The quota needed is 111. P1 has a weightage of 80. If you take weightage of P2, then their weightage sum is 140(80+60) which means the quota is exceeded and the coalition does not fail. Here P2 is the pivotal player since P2's involvement ensured exceeding the quota

3) Count how many times each player is pivotal.

4) Convert these counts to decimals or fractions by dividing the count by total number of sequential coalitions

a) [111:80,60,50,20]

Since there are 4 players, there are total of 4!=24 coalitions

b) [119:80 60 50,20]

c)[120:80,60,50,20]

Player Number of times Pivotal Power index=(number of times)/24 80 10 0.4167 60 6 0.2500 50 6 0.2500 20 2 0.0833
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