Shapley Shubik Power Index Concepts

The video tutorial explains the Shapley-Shubik Power Index, a method for calculating power in weighted voting systems. It contrasts with the Banzhaf Power Index by focusing on pivotal players, who turn a coalition into a winning one. The tutorial covers the concept of sequential coalitions, calculated using factorials, and provides a detailed example with four players. It guides viewers through identifying pivotal players and calculating the power index for each player, emphasizing the unique approach of Shapley-Shubik compared to Banzhaf.

What is the primary purpose of the Shapley Shubik Power Index?

• To identify the most popular player

• To determine the total number of votes in a system

• To calculate the average votes per player

• To measure the influence of players in a voting system

How does the Shapley Shubik Power Index differ from the Banzaf Power Index?

• It identifies the most popular player

• It calculates the total votes differently

• It uses a different method to form coalitions

• It focuses on the least influential player

What is a pivotal player in the context of the Shapley Shubik Power Index?

• A player who turns a coalition into a winning one

• A player with the most votes

• A player who is always critical

• A player who never joins a coalition

What mathematical concept is used to determine the order of sequential coalitions?

• Logarithms

• Exponentials

• Derivatives

• Factorials

In a four-player voting system, how many sequential coalitions are possible?

• 16

• 12

• 8

• 24

What is the quota needed to form a winning coalition in the given example?

• 30

• 15

• 20

• 25

How many pivotal players are identified in each coalition according to the Shapley Shubik method?

• None

• One

• Two

• Three

In the example, which player becomes pivotal when the coalition reaches exactly 20 votes?

• Player 2

• Player 4

• Player 1

• Player 3

What is the total number of underlines used to calculate the Shapley Shubik power index for each player?

• 24

• 20

• 12

• 16

How many times is Player 1 underlined in the example?

• 10

• 4

• 8

• 6