3.6: Exercises(Skills)
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- How many players are there?
- What is the total number (weight) of votes?
- What is the quota in this system?
- Consider the weighted voting system [31: 10,10,8,7,6,4,1,1]
- How many players are there?
- What is the total number (weight) of votes?
- What is the quota in this system?
- Consider the weighted voting system [q: 7,5,3,1,1]
- What is the smallest value that the quota q can take?
- What is the largest value that the quota q can take?
- What is the value of the quota if at least two-thirds of the votes are required to pass a motion?
- Consider the weighted voting system [q: 10,9,8,8,8,6]
- What is the smallest value that the quota q can take?
- What is the largest value that the quota q can take?
- What is the value of the quota if at least two-thirds of the votes are required to pass a motion?
- Consider the weighted voting system [13: 13, 6, 4, 2]
- Identify the dictators, if any.
- Identify players with veto power, if any
- Identify dummies, if any.
- Consider the weighted voting system [11: 9, 6, 3, 1]
- Identify the dictators, if any.
- Identify players with veto power, if any
- Identify dummies, if any.
- Consider the weighted voting system [19: 13, 6, 4, 2]
- Identify the dictators, if any.
- Identify players with veto power, if any
- Identify dummies, if any.
- Consider the weighted voting system [17: 9, 6, 3, 1]
- Identify the dictators, if any.
- Identify players with veto power, if any
- Identify dummies, if any.
- Consider the weighted voting system [15: 11, 7, 5, 2]
- What is the weight of the coalition \left\{P_{1}, P_{2}, P_{4}\right\}
- In the coalition \left\{P_{1}, P_{2}, P_{4}\right\} which players are critical?
- Consider the weighted voting system [17: 13, 9, 5, 2]
- What is the weight of the coalition \left\{P_{1}, P_{2}, P_{3}\right\}
- In the coalition \left\{P_{1}, P_{2}, P_{3}\right\} which players are critical?
- Find the Banzhaf power distribution of the weighted voting system
[27: 16, 12, 11, 3]
- Find the Banzhaf power distribution of the weighted voting system
[33: 18, 16, 15, 2]
- Consider the weighted voting system [q: 15, 8, 3, 1] Find the Banzhaf power distribution of this weighted voting system,
- When the quota is 15
- When the quota is 16
- When the quota is 18
- Consider the weighted voting system [q: 15, 8, 3, 1] Find the Banzhaf power distribution of this weighted voting system,
- When the quota is 19
- When the quota is 23
- When the quota is 26
- Consider the weighted voting system [17: 13, 9, 5, 2]. In the sequential coalition <P_{3}, P_{2}, P_{1}, P_{4}> which player is pivotal?
- Consider the weighted voting system [15: 13, 9, 5, 2]. In the sequential coalition \left\langle P_{1}, P_{4}, P_{2}, P_{3}\right > which player is pivotal?
- Find the Shapley-Shubik power distribution for the system [24: 17, 13, 11]
- Find the Shapley-Shubik power distribution for the system [25: 17, 13, 11]