In the weighted voting system below, the weights represent voters \( \mathrm{A}, \mathrm{B}, \mathrm{C} \), and so on, in that order. Identify a) the quota, b) the number and weights of the voters, c) dictators, and those having veto power. \( [26: 3,3,7,8,9] \) a) The quota is 26 . Pcore: \( 31.43 \%, 11 \) of 35 points b) There are 5 voters. The weights of the voters are (Use a comma to separate answers as needed.)

To analyze the weighted voting system given by \( [26: 3,3,7,8,9] \), we will follow the steps outlined in your request. ### a) The Quota The quota is the minimum number of votes required to pass a motion. From the notation \( [26: 3,3,7,8,9] \), we can see that the quota is \( 26 \). ### b) Number and Weights of the Voters The number of voters is determined by the number of weights provided. In this case, there are 5 voters with the following weights: - Voter A: 3 - Voter B: 3 - Voter C: 7 - Voter D: 8 - Voter E: 9 Thus, the weights of the voters are \( 3, 3, 7, 8, 9 \). ### c) Dictators and Veto Power - **Dictators**: A voter is considered a dictator if their vote alone can determine the outcome of the voting. This means that if a voter has a weight equal to or greater than the quota, they can pass a motion by themselves. In this case, no voter has a weight of 26 or more, so there are no dictators. - **Veto Power**: A voter has veto power if their vote is necessary to reach the quota. This means that if a voter's weight is greater than or equal to the quota minus the sum of the weights of all other voters, they have veto power. Let's calculate the total weight of all voters: \[ 3 + 3 + 7 + 8 + 9 = 30 \] The quota is 26, so the sum of the weights of the other voters must be less than or equal to \( 30 - 26 = 4 \) for a voter to have veto power. Now, we check each voter: - Voter A (weight 3): The sum of the weights of the other voters (3 + 7 + 8 + 9 = 27) is greater than 4. No veto power. - Voter B (weight 3): Same as Voter A. No veto power. - Voter C (weight 7): The sum of the weights of the other voters (3 + 3 + 8 + 9 = 23) is greater than 4. No veto power. - Voter D (weight 8): The sum of the weights of the other voters (3 + 3 + 7 + 9 = 22) is greater than 4. No veto power. - Voter E (weight 9): The sum of the weights of the other voters (3 + 3 + 7 + 8 = 21) is greater than 4. No veto power. Thus, no voter has veto power. ### Summary of Results - a) The quota is \( 26 \). - b) The number of voters is \( 5 \) and the weights of the voters are \( 3, 3, 7, 8, 9 \). - c) There are no dictators and no voters with veto power. Final answers: - a) 26 - b) 5, 3, 3, 7, 8, 9 - c) No dictators, no veto power.