Critical Players in Coalitions

This video tutorial introduces the concepts of coalitions and critical players in weighted voting systems. It explains how a coalition is formed and what makes it a winning coalition. The tutorial provides examples to identify critical players within a coalition, emphasizing the importance of each player's contribution to meeting the quota. It revisits definitions such as dictator, veto power, and dummy player, integrating these concepts with coalitions and critical players.

What is a coalition in a weighted voting system?

• A group of players with equal weights

• A group of players voting differently

• A group of players voting the same way

• A single player voting alone

When is a coalition considered a winning coalition?

• When it includes all players

• When it has more players than any other coalition

• When it has the highest individual weight

• When it has enough weight to meet or exceed the quota

In the first example, which player is NOT critical?

• Player One

• Player Five

• Player Two

• Player Four

What happens if a critical player leaves a coalition?

• The coalition's weight increases

• The coalition remains winning

• The coalition becomes stronger

• The coalition changes from winning to losing

In the second example, what is the combined weight of the coalition?

• 45

• 33

• 54

• 66

Which player is critical in the second example?

• None of the players

• Player Three

• Player Two

• Player One

What defines a player as a dictator in a coalition?

• If they are not critical in any coalition

• If they have the highest weight

• If their single-player coalition is winning

• If they are critical in every coalition

What does it mean if a player has veto power?

• They can remove other players

• They are not critical in any coalition

• They are critical in every winning coalition

• They can change the quota

What is a dummy player in a coalition?

• A player who is critical in every coalition

• A player with the highest weight

• A player who is not critical in any winning coalition

• A player who can change the quota

Which of the following is NOT a characteristic of a critical player?

• Their departure changes a winning coalition to losing

• They have the highest individual weight

• They are essential for the coalition to meet the quota

• Their presence is necessary for a winning coalition