Shapley-Shubik Power Index Concepts

The video tutorial introduces power indices in weighted voting systems, focusing on the Shapley-Shubik power index. It explains how permutations of voters determine the pivotal voter, who is crucial for passing a motion. The tutorial provides examples of weighted voting systems and demonstrates how to calculate the Shapley-Shubik power index using permutations and factorials. It also discusses the concept of dummy voters and dictator voters, highlighting their impact on power indices.

What is the primary focus of the Shapley-Shubik Power Index?

• Measuring the weight of each voter's vote

• Determining the order of voters

• Calculating the actual power of a voter in a weighted voting system

• Identifying the most popular voter

In the context of the Shapley-Shubik Power Index, what is a permutation?

• A way to eliminate voters

• A random selection of voters

• An ordering of voters

• A method to count votes

Who is considered the pivotal voter in a permutation?

• The voter with the highest weight

• The voter who changes their vote last

• The voter whose vote causes the motion to pass

• The voter who votes first

How is the Shapley-Shubik Power Index calculated?

• By counting the total number of votes

• By determining the number of times a voter is pivotal across all permutations

• By adding the weights of all voters

• By subtracting the number of no votes from yes votes

What is the purpose of using tree diagrams in the Shapley-Shubik Power Index?

• To visualize the order of voters

• To illustrate all possible permutations

• To calculate the total number of votes

• To determine the pivotal voter

In a four-voter system, how many permutations are there?

• 48

• 12

• 36

• 24

In the three-voter example, what is the Shapley-Shubik Power Index for a voter who is never pivotal?

• 1

• 0.5

• 0

• 0.25

What is a dummy voter in the context of the Shapley-Shubik Power Index?

• A voter with the highest weight

• A voter who is never pivotal

• A voter who always votes yes

• A voter who is pivotal in every permutation

What is a dictator voter in the context of the Shapley-Shubik Power Index?

• A voter who never votes

• A voter who is pivotal only once

• A voter with the lowest weight

• A voter who is pivotal in every permutation