Lecture2 (1)

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

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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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