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
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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.

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- Spring '08
- SOLFIELL
- Math, Pairwise comparison, majority candidate
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