why isnt anyone answering ASAP Determine all the sequential coalitions and find the shapley shubik power distribution

Question

Determine all the sequential coalitions and find the shapley shubik power distribution

[10.5 : 5,5,6,3]

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Answer 1

Find the shapley shubik power distribution.

Determine all the sequential coalitions and find the shapley shubik power distribution:

First you need to understand the notation [10.5:5,5,6,3]

Quota = the number you need to have to reach your goal or to win

Then you need to get the number of permutations of A,B,C and D and then for each permutation, you need to add the votes from left to right to get the pivotal vote.

example:

In permutation: ABCD

A = 5 (A is not the pivotal vote)

A+B =10 (B is not the pivotal vote)

A+B+C = (C is the pivotal vote because it reaches or passes the goal or quota of 10.5)

In permutation: CBDA

C= 6

C+B = 11 (B is the pivotal vote)

In permutation: BCAD

B = 5

B+C = 11(C is the pivotal vote)

and so on.......

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The number of permutations of A, B,C and D is 4!= 4*3*2*1 = 24

So if you get all the pivotal votes for each permutation, you'll get the following:

A as pivotal -> 5

B as pivotal -> 7

C as pivotal -> 10

D as pivotal -> 2

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Total pivotals->24

The Shapley -Shubik Power Index or Distribution (SSPI) for a voter is the number of times the voter was pivotal divided by the total number of permutation

SSPI(A) = 5/24

SSPI(B) = 7/24

SSPI(C) = 10/24 = 5/12

SSPI(D) = 2/24 = 1/12