KConsider the weighted voting system [18: 15, 14, 3, 1].(a) Which players are critical in the coalition (P₁, P2, P4)?(b) Write down all winning coalitions.(c) Find the Banzhaf power distribution of this weighted voting system.

There are 15 coalitions for a 4 player voting system.CoalitionsWeight…

Answered: Consider the weighted voting system…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For the weighted voting system [12: 8,6,5,3]: a. List all coalitions; identify which are winning coalitions. b. Determine the critical players in each winning coalition. Determine the Banzhaf power distribution for the system. C.
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1.F.5 To any vector v = in R° we can associate a polynomial p„ (x) = ax² + bx + c in P<2. There is a linear transformation R3 → R³ where Pv(3) L(v) =| P.(3) P"(3) For example, when v = we have Рo (г) — 2? + а + 5, р.(3) — 17, pl(2) %— 2л + 1, p.(3) — 7, р"(ӕ) %3D 2, р"(3) — 2 and thus 17 L(v) = 7 Write down a matrix A such that L(v) = A · v.
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The weighted voting systems for the voters A, B, C, ... are given in the form {q: w1, w2, w3, w4, ..., wn}. The weight of voter A is w1, the weight of voter B is w2, the weight of voter C is w3, and so on.Consider the weighted voting system {73: 4, 69, 71}. (a) Compute the Banzhaf power index for each voter in this system. (Round your answers to the nearest hundredth.) BPI(A) = BPI(B) = BPI(C) = (b) Voter B has a weight of 69 compared to only 4 for voter A, yet the results of part (a) show that voter A and voter B both have the same Banzhaf power index. Explain why it seems reasonable, in this voting system, to assign voters A and B the same Banzhaf power index: a) Despite the varied weights, in this system, all of the voters are needed for a quota. b) Despite the varied weights, this is a dictator system. Voter C controls the outcome, while voters A and B are dummy voters. c) Despite the varied weights, in this system, all voters are dummy voters. No voter…
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An executive board consists of a president (P) and three vice-presidents (V1,V2,V3)(V1,V2,V3). For a motion to pass it must have yes votes from three of the voting members, one of which must be the president's.A weighted system that could represent this situation is:[Q:P,V1,V2,V3][Q:P,V1,V2,V3]where:QQ = PP = V1V1 = V2V2 = V3V3 =
The weighted voting systems for the voters A, B, C, ... are given in the form q: w1, w2, w3, w4, ..., wn . The weight of voter A is w1, the weight of voter B is w2, the weight of voter C is w3, and so on.

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Consider the weighted voting system [18: 15, 14, 3, 1]. (a) Which players are critical in the coalition (P₁, P2, P4}? (b) Write down all winning coalitions. (c) Find the Banzhaf power distribution of this weighted voting system.