(1) To verify: That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

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Chapter 2, Problem 68E

To determine

(1)

To verify:

That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

To determine

b.

To explain:

Why two proportional weighted voting systems always have the same Banzhaf power distribution.

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b) Solve the following linear program using the 2-phase simplex algorithm. You should give the initial tableau, and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. maximize ₁ - 2x2+x34x4 subject to 2x1+x22x3x41, 5x1 + x2-x3-×4 ≤ −1, 2x1+x2-x3-34 2, 1, 2, 3, 40.

Suppose we have a linear program in standard equation form maximize cTx subject to Ax = b. x ≥ 0. and suppose u, v, and w are all optimal solutions to this linear program. (a) Prove that zu+v+w is an optimal solution. (b) If you try to adapt your proof from part (a) to prove that that u+v+w is an optimal solution, say exactly which part(s) of the proof go wrong. (c) If you try to adapt your proof from part (a) to prove that u+v-w is an optimal solution, say exactly which part(s) of the proof go wrong.

a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? x1 x2 x3 81 82 83 84 81 -2 0 1 1 0 0 0 3 82 3 0 -2 0 1 2 0 6 12 1 1 -3 0 0 1 0 2 84 -3 0 2 0 0 -1 1 4 -2 -2 0 11 0 0-4 0 -8

Answer 2

Question

Chapter 2, Problem 68E

To determine

(1)

To verify:

That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

To determine

b.

To explain:

Why two proportional weighted voting systems always have the same Banzhaf power distribution.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 2, Problem 68E

To determine

(1)

To verify:

That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

To determine

b.

To explain:

Why two proportional weighted voting systems always have the same Banzhaf power distribution.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 2, Problem 68E

To determine

(1)

To verify:

That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

To determine

b.

To explain:

Why two proportional weighted voting systems always have the same Banzhaf power distribution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 2, Problem 68E

To determine

(1)

To verify:

That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

To determine

b.

To explain:

Why two proportional weighted voting systems always have the same Banzhaf power distribution.

Answer 6

Chapter 2, Problem 68E

To determine

(1)

To verify:

That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

Answer 7

Chapter 2, Problem 68E

To determine

(1)

To verify:

That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

Answer 8

To determine

b.

To explain:

Why two proportional weighted voting systems always have the same Banzhaf power distribution.

Answer 9

To determine

b.

To explain:

Why two proportional weighted voting systems always have the same Banzhaf power distribution.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Prob. 3E Ch. 2 - Prob. 4E Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - Consider the weighted voting system[q:7,5,3]. Find...Ch. 2 - Consider the weighted voting system...Ch. 2 - A committee has four members (P1,P2,P3,andP4). In...Ch. 2 - A committee has six members...

(1) To verify: That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

Solution Summary: The author explains the Shapley-Shubik power index (SSPI) of a player is the ratio of the player's pivotal count over the total pivot

Concept explainers

Videos

(1)

To verify:

That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

b.

To explain:

Why two proportional weighted voting systems always have the same Banzhaf power distribution.

Want to see the full answer?

Chapter 2 Solutions

(1) To verify: That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

Solution Summary: The author explains the Shapley-Shubik power index (SSPI) of a player is the ratio of the player's pivotal count over the total pivot

Concept explainers

Videos

(1) To verify: That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

b. To explain: Why two proportional weighted voting systems always have the same Banzhaf power distribution.

Want to see the full answer?

Chapter 2 Solutions

(1)

To verify:

That the two weighted voting distributions have exactly same Shapley-Shubik power distribution.

b.

To explain:

Why two proportional weighted voting systems always have the same Banzhaf power distribution.