Pivotal Players in Coalitions

The video tutorial explains the Shapley-Shubik power index in a weighted voting system. It begins by introducing the concept of sequential coalitions and the importance of identifying pivotal players. The tutorial then lists all possible permutations of players and determines which player is pivotal in each coalition. Finally, it calculates the Shapley-Shubik power index by counting how many times each player is pivotal and converting these counts into fractions or percentages.

What is the primary focus of the Shapley-Shubik power index?

• Calculating the average weight of players

• Identifying the pivotal player in each coalition

• Listing all possible coalitions

• Determining the total weight of all players

What distinguishes sequential coalitions from regular coalitions?

• They only include two players

• They ignore the weight of players

• They are based on random selection

• They consider the order of players

How many sequential coalitions are possible with three players?

• Six

• Five

• Four

• Three

In the coalition P1, P3, P2, which player is pivotal?

• Player 1

• Player 2

• Player 3

• None

What is the weight of Player 1 in the coalition P2, P1, P3?

• 4

• 5

• 3

• 2

In the coalition P3, P2, P1, which player is pivotal?

• Player 3

• Player 2

• None

• Player 1

Which player is pivotal in the coalition P2, P3, P1?

• Player 2

• Player 3

• None

• Player 1

What is the weight of Player 3 in the coalition P1, P3, P2?

• 2

• 1

• 3

• 4

In the coalition P3, P1, P2, which player is pivotal?

• Player 1

• Player 2

• Player 3

• None

How many times is Player 1 pivotal across all coalitions?

• Three times

• Four times

• Twice

• Once