Lecture2 (1) - REVIEW VotingMethod VotingData>VotingOutcome...

REVIEW
Voting Method
Voting Data ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­> Voting Outcome
Voting Data : Single Choice
Preference Schedule
Voting Outcome: Winner Only
Full (or Partial) Ranking
Voting Method: 1) Plurality
2) Borda Count
3) Plurality with Elimination (Today)
4) Pairwise Comparison (Hopefully)
Borda Count (again):
We have N candidates
1,2,3,4, ..... , N­1, N
ex. (N=5) 1,2,3,4,5
ex. (N=8) 1,2,3,4,5,6,7,8
Each ‘place’ gets a set number of points, counting backwards from N:
(Place) 1,2,3,4,5,6,7,8,9
| | | | | | | | |
(Points) 9,8,7,6,5,4,3,2,1
2 examples:
1st place 5 points 1st 4 points
2nd place 4 points 2nd 3 points
3rd place 3 points 3rd 2 points

4th place 2 points 4th (Last) 1 point
5th (Last) 1 point
Ballot 1 Ballot 2 ... Last Ballot
Score = (# votes)(# points) + (# votes)(# points) + ... + (#votes)(# points)
Cherry = ( 5 ) ( 1 )+( 3 )( 4 )+( 6 ) ( 1 )+( 2 ) ( 1 )+( 4 ) ( 3 ) = 37
Grape = ( 5 ) ( 3 )+( 3 )( 2 )+( 6 ) ( 4 )+( 2 ) ( 3 )+( 4 ) ( 4 ) = 67
Sour = ( 5 ) ( 4 )+( 3 )( 1 )+ ( 6 ) ( 3 )+( 2 ) ( 2 )+( 4 ) ( 2 ) = 50
Wate = ( 5 ) ( 2 )+( 3 )( 3 )+ ( 6 ) ( 2 )+( 2 ) ( 4 )+( 4 ) ( 1 ) = 43
The winner in this case is Grape.
Modified Borda Count: (Homework 30)
Each ‘place’ gets a set number of points, ranked highest to lowest, but we
are allowed to CHOOSE which points.
Example:
(Place) 1,2,3,4
| | | |
(Points) 7,5,2,1
Cherry = ( 5 ) ( 1 )+( 3 )( 7 )+( 6 ) ( 1 )+( 2 ) ( 1 )+( 4 ) ( 5 ) = 54
Grape = ( 5 ) ( 5 )+( 3 )( 2 )+( 6 ) ( 7 )+( 2 ) ( 5 )+( 4 ) ( 7 ) = 111
Sour = ( 5 ) ( 7 )+( 3 )( 1 )+ ( 6 ) ( 5 )+( 2 ) ( 2 )+( 4 ) ( 2 ) = 80
Wate = ( 5 ) ( 2 )+( 3 )( 5 )+ ( 6 ) ( 2 )+( 2 ) ( 7 )+( 4 ) ( 1 ) = 55
The winner again is Grape. Sometimes its a different winner.