Voting Ranked Pairs and Copelands Method Copelands Method

Voting Ranked Pairs and Copeland’s Method

Copeland’s Method

Background � Uses preferences � If there isn’t a Condorcet winner, ties may happen � Puts emphasis on paired wins/losses, not magnitudes

Method � Compare each candidate against all others � Computer the “winner” of each pair � Sort the candidates by wins-losses

Example � Using the following voter preferences from class on Tuesday: � P > D > S > C: 7 C > D > S > P: 4 S > D > C > P: 6 D > C > S > P: 3

Paired Results Candidates Result Winner Pepsi vs Coke 7 -13 Coke Pepsi vs Sprite 7 -13 Sprite Pepsi vs. vs Dr. Pepper 7 -13 Dr. Pepper Coke vs. Sprite 7 -13 Sprite Coke vs. Dr. Pepper 4 -16 Dr. Pepper Sprite vs. Dr. Pepper 6 -14 Dr. Pepper P > D > S > C: C > D > S > P: S > D > C > P: D > C > S > P: 7 4 6 3

Wins and Losses Brand Wins Losses Wins - Losses Pepsi 0 3 -3 Coke 1 2 -1 Sprite 2 1 1 Dr. Pepper 3 0 3

Conclusion � Dr. Pepper wins! � Note that, in this situation, Dr. Peppers is also the Condorcet winner.

Ranked Pairs

Background � Developed in 1987 by Nicolaus Tideman � Uses preferences � Chooses a single winner � Can also be used to create an ordered list of results � Condorcet method

Method � Compare each candidate against all others � Computer the “winner” of each pair � Sort the pairs by largest margin of victory � Iterate through list, selecting any that don’t create a cycle. � The completed graph shows the winner

Example � Using the following voter preferences from class on Tuesday: � P > D > S > C: 7 C > D > S > P: 4 S > D > C > P: 6 D > C > S > P: 3

Paired Results Pepsi X Coke Sprite Dr. Pepper 13 – 7 13 - 7 13 – 7 16 – 4 Coke 7 - 13 X Sprite 7 - 13 Dr. Pepper 7 - 13 4 - 16 6 – 14 RECORD: 0– 3 -0 1– 2 -0 2– 1 -0 X P > D > S > C: C > D > S > P: S > D > C > P: D > C > S > P: 7 4 6 3 14 – 6 X 3– 0– 0

Tallying Votes Brand A Brand B Winner Pepsi Coke (13 votes) Pepsi Sprite (13 votes) Pepsi Dr. Pepper (13 votes) Coke Sprite (13 votes) Coke Dr. Pepper (16 votes) Sprite Dr. Pepper (14 votes)

Sorted Tally Brand A Brand B Winner Coke Dr. Pepper (16 votes) Sprite Dr. Pepper (14 votes) Pepsi Coke (13 votes) Pepsi Sprite (13 votes) Pepsi Dr. Pepper (13 votes) Coke Sprite (13 votes)

Ranking Diagram

Conclusion � Dr. Pepper is the winner! � All other sodas are preferred to Pepsi � To create a ranked list, remove the winner (Dr. Pepper) and repeat.