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5 October, 07:52

Find a simplified weighted voting system which is equivalent to

[8: 9, 3, 2, 1] and

[20: 8, 6, 3, 2, 1].

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  1. 5 October, 08:05
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    Answer: The explanation is as follows:

    Step-by-step explanation:

    (a) [8: 9, 3, 2, 1]

    q = 8

    Here, coalition is as follows:

    [P1, P2, P3, P4] = [9, 3, 2, 1]

    for the above coalition, the combined weight is

    [P1, P2, P3, P4] = 9+3+2+1 = 15 ⇒ combined weight

    For simplified weighted voting system;

    q = combined weight ⇒ both the terms have to be equal for a simplified weighted voting system.

    But, here 8 ≠ 15

    ∴ It is not a simplified weighted voting system.

    (b) [20: 8, 6, 3, 2, 1]

    q = 20

    Here, coalition is as follows:

    [P1, P2, P3, P4, P5] = [8, 6, 3, 2, 1]

    for the above coalition, the combined weight is

    [P1, P2, P3, P4, P5] = 8+6+3+2+1 = 20 ⇒ combined weight

    For simplified weighted voting system;

    q = combined weight

    Since, 20 = 20

    ∴ It is a simplified weighted voting system.
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