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In the weighted voting system below, the weights represent voters A, B, C, and so on, in that order. Identify a) the quota, b) the number and weights of the voters, c) dictators, and d) those having veto power. \( [26: 3,3,7,8,9] \) b) There are 5 voters. The weights of the voters are \( 3,3,7,8,9 \). (Use a comma to separate answers as needed.) c) Identify any dictators, Select the correct choice below and fill in any answer boxes within your choice. B. There are no dictators. The dictator(s) is(are) (Use a comma to separate answers as needed.) d) Identity any voters that have veto power. Select the correct choice below and fill in any answer boxes within your choice. (o) A. The voter(s) with veto power is(are) \( \square \) (Use a comma to separate answers as needed.)

Ask by Chang Harris. in the United States
Feb 13,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

a) The quota is 26. b) There are 5 voters with weights: A = 3, B = 3, C = 7, D = 8, E = 9. c) There are no dictators. d) Voters C, D, and E have veto power.

Solution

a) The quota is 26. b) There are 5 voters with weights: A = 3, B = 3, C = 7, D = 8, E = 9. c) There are no dictators. d) A voter has veto power if every winning coalition must include that voter.   – Consider voter E (9): Without E, the maximum total weight from A, B, C, and D is 3 + 3 + 7 + 8 = 21, which is less than 26. Therefore, every winning coalition must include E.   – Similarly, without D (8): A, B, C, and E together sum to 3 + 3 + 7 + 9 = 22, less than 26. So, D is essential.   – Without C (7): A, B, D, and E add up to 3 + 3 + 8 + 9 = 23, still less than 26. Thus, C is also needed. Voters A and B do not have veto power because, for example, the coalition B, C, D, and E (totaling 3 + 7 + 8 + 9 = 27) wins without A, and similarly for B. So, the voters with veto power are C, D, and E.

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The Deep Dive

a) The quota is 14. B. There are 5 voters. The weights of the voters are \( 3,3,7,8,9 \). B. There are no dictators. The dictator(s) is(are) none. A. The voter(s) with veto power is(are) C, D, E.

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