1 / 8

Discrete Math

Discrete Math. CHAPTER TWO. 2.1 Weighted Voting: One voter - x votes. Ex. Electoral College. Weighted Voting System: Any formal voting arrangement in which the voters are not necessarily equal in terms of the final number of votes they control. Motion: A yes/no vote. Players: The voters

razi
Télécharger la présentation

Discrete Math

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Discrete Math CHAPTER TWO 2.1 • Weighted Voting: One voter - x votes. Ex. Electoral College. • Weighted Voting System: Any formal voting arrangement in which the voters are not necessarily equal in terms of the final number of votes they control. • Motion: A yes/no vote. • Players: The voters • Weight: Number of votes the player controls. To be continued…

  2. Discrete Math CHAPTER TWO 2.1 (Continued...) • Quota: The minimum number of votes needed to pass a motion. • May be something other than the majority. • Notation: [Q :w1, w2, w3, ...] • Dictator: A player that has a weight equal to or larger than the quota. • Dummy: A player with no power. • Veto Power: A player that is not a dictator, but can single-handedly prevent the rest of the players from passing a motion.

  3. Discrete Math CHAPTER TWO 2.2 • Banzhaf Power Index: Method of calculation Power. • Coalition: Any set of players that might join forces to vote together. • Winning Coalition: Has enough votes to win. • Losing Coalition: Does not have enough votes to win. • Critical Player: Players whose desertion turns a winning coalition into a losing coalition. To be continued…

  4. Discrete Math CHAPTER TWO 2.2 (Continued...) • Steps: • One: Make a list of all possible coalitions. • Two: Determine which of the above are winning coalitions. • Three: Determine the critical players in each winning coalition. • Four: Count the number of times each player is critical (B). • Five: Count the total of times all players are critical() and create the power for each player as B/T… may write as percentage. To be continued…

  5. Discrete Math CHAPTER TWO 2.2 (Continued...) • Number of possible coalitions: 2n-1 • Sometimes we can save ourselves a lot of work by figuring out directly which are the winning coalitions instead of listing all of them. Range of Quota: Sum of weights / 2 < Q <= Sum of weights

  6. Discrete Math CHAPTER TWO 2.3 • Shapley-Shubik Power Index: • Sequential Coalition: Difference in Shapley-Shubik and Banzhaf, coalitions are assumed to be formed sequentially. • The Number of Sequential Coalitions: N! • Pivotal Player: The player joins the coalition and causes the coalition to change from losing to winning. To be continued…

  7. Discrete Math CHAPTER TWO 2.3 (Continued...) • Steps: • One: Make a list of all sequential coalitions. • Two: In each coalition determine the pivotal player. • Three: Count the total number of times P is pivotal and call this number S. The Shapley-Shubik power index of each player will be calculated as S/N!. (Fraction or Percentage)

  8. 2 End of Chapter Discrete Math CHAPTER TWO

More Related