A simplified version of the 2018 Canadian senate was [53:43,33,12,11,6]. compute the Shapley Shubik index of...

A simplified version of the 2018 Canadian senate was [53:43,33,12,11,6].

compute the Shapley Shubik index of the party with 43 votes.

Expert Solution

Let us make a list of permutations of voters

there are 5!=120 coalations possible

43	33	12	11	6
33	43	12	11	6
33	43	11	12	6
43	33	11	12	6
43	33	6	12	11
33	43	6	12	11
33	43	12	6	11
43	33	12	6	11
33	43	6	11	12
43	33	6	11	12
43	33	11	6	12
33	43	11	6	12
12	43	33	11	6
43	12	33	11	6
43	12	11	33	6
12	43	11	33	6
43	12	33	6	11
12	43	33	6	11
12	43	6	33	11
43	12	6	33	11
43	12	6	11	33
12	43	6	11	33
12	43	11	6	33
43	12	11	6	33
11	43	12	33	6
43	11	12	33	6
43	11	33	12	6
11	43	33	12	6
43	11	6	33	12
11	43	6	33	12
11	43	33	6	12
43	11	33	6	12
11	43	6	12	33
43	11	6	12	33
43	11	12	6	33
11	43	12	6	33
33	12	43	11	6
12	33	43	11	6
12	33	43	6	11
33	12	43	6	11
11	33	43	12	6
33	11	43	12	6
33	11	43	6	12
11	33	43	6	12
6	43	33	12	11
43	6	33	12	11
43	6	33	11	12
6	43	33	11	12
33	6	43	12	11
6	33	43	12	11
6	33	43	11	12
33	6	43	11	12
12	11	43	33	6
11	12	43	33	6
11	12	43	6	33
12	11	43	6	33
43	6	12	33	11
6	43	12	33	11
6	43	12	11	33
43	6	12	11	33
6	12	43	33	11
12	6	43	33	11
12	6	43	11	33
6	12	43	11	33
6	43	11	33	12
43	6	11	33	12
43	6	11	12	33
6	43	11	12	33
11	6	43	33	12
6	11	43	33	12
6	11	43	12	33
11	6	43	12	33
12	33	11	43	6
33	12	11	43	6
33	12	11	6	43
12	33	11	6	43
33	11	12	43	6
11	33	12	43	6
11	33	12	6	43
33	11	12	6	43
11	12	33	43	6
12	11	33	43	6
12	11	33	6	43
11	12	33	6	43
33	12	6	43	11
12	33	6	43	11
6	33	12	43	11
33	6	12	43	11
12	6	33	43	11
6	12	33	43	11
11	33	6	43	12
33	11	6	43	12
33	6	11	43	12
6	33	11	43	12
6	11	33	43	12
11	6	33	43	12
12	11	6	43	33
11	12	6	43	33
6	12	11	43	33
12	6	11	43	33
11	6	12	43	33
6	11	12	43	33
12	33	6	11	43
33	12	6	11	43
33	6	12	11	43
6	33	12	11	43
6	12	33	11	43
12	6	33	11	43
33	11	6	12	43
11	33	6	12	43
6	33	11	12	43
33	6	11	12	43
11	6	33	12	43
6	11	33	12	43
11	12	6	33	43
12	11	6	33	43
12	6	11	33	43
6	12	11	33	43
6	11	12	33	43
11	6	12	33	43

the hilighted cells are pivot voters. party with 43 votes is pivot in 60 coalations out of 120.

so the shapley shubix index of party with 43 votes is = 60/120 = 1/2

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