Understanding the Shapley-Shubik Power Index

The video tutorial introduces the Shapley-Shubik Power Index, a method developed in 1954 by economists Lloyd Shapley and Martin Shubik to calculate power in weighted voting systems. It emphasizes the importance of the order in which players join coalitions, defining pivotal players as those who change a coalition from losing to winning. The tutorial outlines steps to calculate the Shapley-Shubik Power Index, provides an example calculation, and compares it with the Banzhaf Power Index, highlighting their differences.

Who introduced the Shapley-Shubik Power Index?

• Martin Shubik and John Nash

• John Nash and Martin Shubik

• Lloyd Shapley and John Nash

• Lloyd Shapley and Martin Shubik

What is the main difference between the Shapley-Shubik and Banzhaf Power Index?

• The Banzhaf Index is used only in economic models.

• The Shapley-Shubik is used only in political alliances.

• The Banzhaf Index considers the order of players joining a coalition.

• The Shapley-Shubik considers the order of players joining a coalition.

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

• A player with the highest weight in a coalition.

• A player who leaves a coalition last.

• A player who changes a coalition from losing to winning.

• A player who joins a coalition first.

What is the first step in calculating the Shapley-Shubik Power Index?

• Calculate the total weight of the coalition.

• Count the number of players.

• List all sequential coalitions.

• Determine the pivotal player.

How many sequential coalitions are there for a voting system with three players?

• 3

• 6

• 9

• 12

In the example calculation, which player was pivotal the most times?

• Player One

• All players equally

• Player Two

• Player Three

What is the Shapley-Shubik Power Index for Player One in the example?

• 2/3

• 5/6

• 1/3

• 1/6

How is the Shapley-Shubik Power Index expressed?

• Only as a fraction

• Only as a percentage

• As a fraction, decimal, or percentage

• Only as a decimal

What is a key similarity between the Shapley-Shubik and Banzhaf Power Index?

• Both are used exclusively in political contexts.

• Both are identical in calculation.

• Both are used in weighted voting systems.

• Both consider the order of players joining.

Why are the values of the Shapley-Shubik and Banzhaf Power Index often different?

• They are used in different types of voting systems.

• They are calculated by different people.

• They consider different aspects of player influence.

• They use different mathematical formulas.