Banzhaf and Shapley-Shubik Methods

The video tutorial explains the Shapley-Shubik and Banzhaf power indices in weighted voting systems. It highlights the concept of sequential coalitions, where the order of players matters, and introduces the idea of pivotal players who change a coalition from losing to winning. The tutorial provides a step-by-step guide to calculating the Shapley-Shubik power index and compares it with the Banzhaf method, noting their differences and similarities.

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

• Shapley-Shubik considers sequential coalitions, Banzhaf does not.

• Banzhaf considers sequential coalitions, Shapley-Shubik does not.

• Neither considers sequential coalitions.

• Both consider sequential coalitions.

In the context of the Shapley-Shubik method, what is a sequential coalition?

• A coalition where the order of players matters.

• A coalition that includes only winning players.

• A coalition that is always non-winning.

• A coalition that excludes the pivotal player.

How many sequential coalitions are there for four players?

• 48

• 24

• 12

• 6

What defines a pivotal player in a sequential coalition?

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

• A player who is always included in the coalition.

• A player who can be removed without affecting the outcome.

• A player who has the least weight.

How does the Banzhaf Power Index differ in calculation from the Shapley-Shubik Power Index?

• Banzhaf requires permutations, Shapley-Shubik does not.

• Both require permutations.

• Shapley-Shubik requires permutations, Banzhaf does not.

• Neither requires permutations.

What is a noted advantage of the Banzhaf method over the Shapley-Shubik method?

• It is easier to understand.

• It considers more players.

• It requires fewer calculations.

• It is more accurate.