Pivotal Players in Voting Systems

The video tutorial explores the concept of power in weighted voting systems, focusing on when coalitions become winning coalitions and the role of pivotal players. It introduces sequential coalitions, where the order of players joining affects the outcome, and explains how to identify the pivotal player who tips the balance of power. The Shapley-Shubik power index is presented as a method to measure the power of players in these systems, with examples illustrating the process of listing sequential coalitions, identifying pivotal players, and calculating power distribution.

What is the main focus when measuring power in a weighted voting system?

• The critical moments when coalitions become winning

• The number of players in the system

• The order of players in a coalition

• The total number of votes

Why is the order of players important in a coalition?

• It affects the balance of power

• It determines the total number of votes

• It decides the number of players

• It changes the voting system

What is a sequential coalition?

• A list of players in a random order

• A list of players in the order they join a coalition

• A list of players in alphabetical order

• A list of players based on their votes

How is a sequential coalition represented?

• With square brackets

• With curly brackets

• With pointy brackets

• With parentheses

What is the role of a pivotal player in a coalition?

• To join the coalition last

• To make the coalition a winning one

• To be the first to join the coalition

• To have the most votes

Can there be more than one pivotal player in a coalition?

• No, there can only be one

• Yes, always

• No, unless the coalition is large

• Yes, if the votes are equal

In the example given, which player was pivotal when player four joined the coalition?

• Player four

• Player three

• Player two

• Player one

What is the Shapley-Shubik power index used for?

• To determine the order of players

• To list all players in a coalition

• To measure the power of pivotal players

• To count the total votes

What is the first step in calculating the Shapley-Shubik power index?

• Determine the pivotal players

• Divide by the total number of players

• List all sequential coalitions

• Count the total votes

In the example, how many times was player one pivotal?

• Once

• Three times

• Twice

• Never