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Chapter 3 Voting and Elections ,[object Object],[object Object],[object Object]
Voting Systems ,[object Object],[object Object],[object Object],[object Object],[object Object]
Voting Systems ,[object Object],[object Object]
Voting Systems ,[object Object]
Voting Systems ,[object Object],[object Object],[object Object],[object Object],[object Object]
Voting Systems ,[object Object],Skittles Reese’s Nestle Crunch Butterfinger 4th place votes 3rd place votes 2nd place votes 1st place votes
Borda Count Method ,[object Object]
Calculate the winning candy bar using the Borda Count Method Candy bar with the most total points is: _______________ Skittles Reese’s Nestle Crunch #votes x 1 = #votes x 2 = #votes x 3 = #votes x 4 = Butterfinger 4th place votes 3rd place votes 2nd place votes 1st place votes
Borda Count Method ,[object Object]
Borda Count Method ,[object Object]
Plurality With Elimination Method ,[object Object],[object Object]
Plurality With Elimination Method ,[object Object]
Plurality With Elimination Method ,[object Object],[object Object],[object Object]
Plurality With Elimination Method ,[object Object],[object Object],[object Object]
Plurality With Elimination Method ,[object Object]
Plurality With Elimination Method ,[object Object],[object Object],[object Object]
Plurality With Elimination Method ,[object Object],[object Object]
Pairwise Comparison Method ,[object Object],[object Object]
Pairwise Comparison Method ,[object Object],[object Object],[object Object],[object Object],[object Object]
Pairwise Comparison Method ,[object Object]
Pairwise Comparison Method ,[object Object],[object Object]
Pairwise Comparison Method ,[object Object]
Section 3.1  Voting Systems ,[object Object],[object Object]
Flaws in Voting Systems ,[object Object],[object Object],[object Object],[object Object],[object Object]
Majority Criterion ,[object Object]
Majority Criterion P B B C P 4th C C S P B 3rd B S P B S 2nd S P C S C 1st 1 1 2 2 3 Ranking members committee planning No. of
Which site would be chosen based on a majority of first-place votes? P B B C P 4th C C S P B 3rd B S P B S 2nd S P C S C 1st 1 1 2 2 3 Ranking members committee planning No. of
Which site would be chosen based on a majority of first-place votes? Chicago: 3 + 2 (first place votes ) = 5 Phoenix: 1 vote Seattle: 2 + 1 = 3 Boston: 0 votes P B B C P 4th C C S P B 3rd B S P B S 2nd S P C S C 1st 1 1 2 2 3 Ranking members committee planning No. of
Which site would be chosen by the Borda count method? P B B C P 4th C C S P B 3rd B S P B S 2nd S P C S C 1st 1 1 2 2 3 Ranking members committee planning No. of
Which site would be chosen by the Borda count method? Chicago: (5x4)+(0x3)+(2x2)+(2x1) = 26 pts  Phoenix: (1x4)+(2x3)+(2x2)+(4x1) = 18 pts Seattle: (3x4)+(4x3)+(2x2)+(0x1) = 28 pts  Boston: (0x4)+(3x3)+(3x2)+(3x1) = 18 pts P B B C P 4th C C S P B 3rd B S P B S 2nd S P C S C 1st 1 1 2 2 3 Ranking members committee planning No. of
Majority Criterion ,[object Object],[object Object],[object Object]
Head-to-Head Criterion ,[object Object]
Head-to-Head Criterion ,[object Object],P P C 3rd R C R 2nd C R P 1st 2 2 3 Ranking members Accounting dept. Number of
Head-to-Head Criterion ,[object Object],P P C 3rd R C R 2nd C R P 1st 2 2 3 Ranking members Accounting dept. Number of
Head-to-Head Criterion ,[object Object],[object Object],P P C 3rd R C R 2nd C R P 1st 2 2 3 Ranking members Accounting dept. Number of
Head-to-Head Criterion ,[object Object],P P C 3rd R C R 2nd C R P 1st 2 2 3 Ranking members Accounting dept. Number of
Head-to-Head Criterion ,[object Object],[object Object],[object Object],[object Object],P P C 3rd R C R 2nd C R P 1st 2 2 3 Ranking members Accounting dept. Number of
Head-to-Head Criterion ,[object Object],[object Object],P P C 3rd R C R 2nd C R P 1st 2 2 3 Ranking members Accounting dept. Number of
Monotonicity Criterion ,[object Object]
Monotonicity Criterion ,[object Object],A B C B 3rd B A A C 2nd C C B A 1st 10 5 12 14 Ranking teachers of Number
Monotonicity Criterion ,[object Object],A B C B 3rd B A A C 2nd C C B A 1st 10 5 12 14 Ranking teachers of Number
Monotonicity Criterion ,[object Object],[object Object],[object Object],A B C B 3rd B A A C 2nd C C B A 1st 10 5 12 14 Ranking teachers of Number
Monotonicity Criterion ,[object Object],A C 2nd C A 1st 15 26 Ranking teachers Number of
Monotonicity Criterion ,[object Object],A B C B 3rd B A A C 2nd C C B A 1st 10 5 12 14 Ranking teachers of Number
Monotonicity Criterion ,[object Object],[object Object],A B C B 3rd B A A C 2nd C C B A 1st 10 1 12 18 Ranking teachers of Number
Monotonicity Criterion ,[object Object],[object Object],[object Object],A B C B 3rd B A A C 2nd C C B A 1st 10 1 12 18 Ranking teachers of Number
Monotonicity Criterion Now B is elected president!  (B was eliminated in the first process.) The Monotonicity Criterion has been violate. A B 2nd B A 1st 22 19 Ranking teachers Number of
Irrelevant-Alternatives Criterion ,[object Object]
Irrelevant-Alternatives Criterion ,[object Object],M S H 3rd H M S 2nd S H M 1st 2 1 2 Ranking members Book club Number of
Irrelevant-Alternatives Criterion ,[object Object],M S H 3rd H M S 2nd S H M 1st 2 1 2 Ranking members Book club Number of
Irrelevant-Alternatives Criterion ,[object Object],[object Object],[object Object],M S H 3rd H M S 2nd S H M 1st 2 1 2 Ranking members Book club Number of
Irrelevant-Alternatives Criterion ,[object Object],M S 2nd S M 1st 2 3 Ranking Club Members Number of
Irrelevant-Alternatives Criterion ,[object Object],M H 2nd H M 1st 3 2 Ranking Club Members Number of
Irrelevant-Alternatives Criterion ,[object Object],[object Object],[object Object],M H 2nd H M 1st 3 2 Ranking Club Members Number of
Flaws in Voting Systems ,[object Object]
Flaws in Voting Systems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Approval Voting One more system ,[object Object],[object Object],[object Object]
Section 3.2 Flaws of Voting Systems ,[object Object]
Weighted Voting Systems ,[object Object],[object Object],[object Object]
Weighted Voting Systems ,[object Object],[object Object],[object Object]
Weighted Voting Systems ,[object Object],[object Object],11 Darrell 8 Carlos 12 Roberta 9 Angie Weight Voter
Weighted Voting Systems ,[object Object],[object Object],[object Object],11 Darrell 8 Carlos 12 Roberta 9 Angie Weight Voter
Weighted Voting Systems ,[object Object],[object Object]
Weighted Voting Systems ,[object Object],[object Object],[object Object],[object Object],[object Object]
Weighted Voting Systems ,[object Object],[object Object],[object Object],[object Object]
Winning and Losing Coalitions ,[object Object]
Winning and Losing Coalitions   [8 | 6, 5, 4]  Winning 6+5+4=15 {P 1 ,P 2 ,P 3 } Winning 5+4=9 {P 2 ,P 3 } Winning 6+4=10 {P 1 ,P 3 } Winning 6+5=11 {P 1 ,P 2 } Losing 4 {P 3 } Losing 5 {P 2 } Losing 6 {P 1 } Winning or Losing Sum of Weights Coalition
Winning and Losing Coalition Given  n  voters, 2 n  - 1 coalitions are possible. 3+3+1=7 See previous list 3 1+1+1=3 {P 1 } {P 2 } {P 1 ,P 2 } 2 1 {P 1 } 1 Number of  Coalitions Coalitions Number of Voters
Weighted Voting Systems ,[object Object]
Weighted Voting Systems ,[object Object],[object Object]
Weighted Voting Systems ,[object Object],[object Object],[object Object],[object Object]
Weighted Voting Systems ,[object Object],[object Object],[object Object]
Weighted Voting Systems ,[object Object],[object Object],[object Object]
Weighted Voting Systems ,[object Object],[object Object]
Section 3.3 Weighted Voting Systems ,[object Object]
Contemporary Math Chapter 3 Assignments ,[object Object],[object Object],[object Object],[object Object]

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Nossi ch 3

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  • 5.
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  • 8. Calculate the winning candy bar using the Borda Count Method Candy bar with the most total points is: _______________ Skittles Reese’s Nestle Crunch #votes x 1 = #votes x 2 = #votes x 3 = #votes x 4 = Butterfinger 4th place votes 3rd place votes 2nd place votes 1st place votes
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  • 26. Majority Criterion P B B C P 4th C C S P B 3rd B S P B S 2nd S P C S C 1st 1 1 2 2 3 Ranking members committee planning No. of
  • 27. Which site would be chosen based on a majority of first-place votes? P B B C P 4th C C S P B 3rd B S P B S 2nd S P C S C 1st 1 1 2 2 3 Ranking members committee planning No. of
  • 28. Which site would be chosen based on a majority of first-place votes? Chicago: 3 + 2 (first place votes ) = 5 Phoenix: 1 vote Seattle: 2 + 1 = 3 Boston: 0 votes P B B C P 4th C C S P B 3rd B S P B S 2nd S P C S C 1st 1 1 2 2 3 Ranking members committee planning No. of
  • 29. Which site would be chosen by the Borda count method? P B B C P 4th C C S P B 3rd B S P B S 2nd S P C S C 1st 1 1 2 2 3 Ranking members committee planning No. of
  • 30. Which site would be chosen by the Borda count method? Chicago: (5x4)+(0x3)+(2x2)+(2x1) = 26 pts Phoenix: (1x4)+(2x3)+(2x2)+(4x1) = 18 pts Seattle: (3x4)+(4x3)+(2x2)+(0x1) = 28 pts Boston: (0x4)+(3x3)+(3x2)+(3x1) = 18 pts P B B C P 4th C C S P B 3rd B S P B S 2nd S P C S C 1st 1 1 2 2 3 Ranking members committee planning No. of
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  • 47. Monotonicity Criterion Now B is elected president! (B was eliminated in the first process.) The Monotonicity Criterion has been violate. A B 2nd B A 1st 22 19 Ranking teachers Number of
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  • 67. Winning and Losing Coalitions [8 | 6, 5, 4] Winning 6+5+4=15 {P 1 ,P 2 ,P 3 } Winning 5+4=9 {P 2 ,P 3 } Winning 6+4=10 {P 1 ,P 3 } Winning 6+5=11 {P 1 ,P 2 } Losing 4 {P 3 } Losing 5 {P 2 } Losing 6 {P 1 } Winning or Losing Sum of Weights Coalition
  • 68. Winning and Losing Coalition Given n voters, 2 n - 1 coalitions are possible. 3+3+1=7 See previous list 3 1+1+1=3 {P 1 } {P 2 } {P 1 ,P 2 } 2 1 {P 1 } 1 Number of Coalitions Coalitions Number of Voters
  • 69.
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