Shapley-Shubik and Banzhaf Indices

The video tutorial explains the weighted voting system with a quota of four, using the Shapley-Shubik power distribution method. It details how to form sequential coalitions and identify pivotal players, then calculates the frequency of each player being pivotal. The tutorial compares the Shapley-Shubik and Banzhaf power indices, highlighting the differences in player influence. The video concludes with a comparison of the two methods, showing that while similar, the Shapley-Shubik index gives player one a slightly higher influence.

What is the quota in the weighted voting system discussed?

• Four

• Five

• Three

• Two

What are the weights of the players in the system?

• 2, 3, 1

• 3, 2, 1

• 1, 3, 2

• 1, 2, 3

What is the weight of player three?

• Four

• One

• Two

• Three

What is the weight of player two?

• Four

• Three

• Two

• One

What is the main concept behind the Shapley-Shubik power distribution?

• Unanimous decision

• Majority rule

• Sequential coalitions

• Random selection

In the Shapley-Shubik method, what is a pivotal player?

• The player who meets the quota

• The first player in the coalition

• The last player in the coalition

• The player with the highest weight

In the first sequential coalition, which player is pivotal?

• Player 1

• Player 2

• None

• Player 3

In the coalition of players one, three, and two, who is pivotal?

• Player 1

• Player 2

• None

• Player 3

In the coalition of players two, one, and three, who is pivotal?

• None

• Player 2

• Player 1

• Player 3

In the coalition of players three, one, and two, who is pivotal?

• None

• Player 2

• Player 1

• Player 3