3.6: Exercises(Skills)
( \newcommand{\kernel}{\mathrm{null}\,}\)
- Consider the weighted voting system [47:10,9,9,5,4,4,3,2,2]
- 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 {P1,P2,P4}
- In the coalition {P1,P2,P4} which players are critical?
- Consider the weighted voting system [17:13,9,5,2]
- What is the weight of the coalition {P1,P2,P3}
- In the coalition {P1,P2,P3} 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 <P3,P2,P1,P4> which player is pivotal?
- Consider the weighted voting system [15:13,9,5,2]. In the sequential coalition ⟨P1,P4,P2,P3⟩ 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]