Who Is Your Favorite Muppet

Chapter 1 VOTING Practice Multiple Choice Use the following preference schedule to answer questions #1 - 10: Voters 8 5 6 3 9 1st A A B C D 2nd B D C B B 3rd C C D A A 4th D B A D C 1) How many candidates are in this election? (rows) A) 5 B) 4 C) 31 D) 16 E) None of the above.

2) How many distinct ballots were cast? (columns) A) 5 B) 4 C) 31 D) 16 E) None of the above.

3) How many people voted in this election? A) 5 B) 4 C) 31 D) 16 E) None of the above.

4) Using the plurality method, who is the winner? A) A=13 B) B = 6 C) C = 3 D) D = 9 E) None of the above.

5) Using the plurality-with-elimination method, who was eliminated 1st? A) A B) B C) C D) D E) None of the above.

6) Using the method of pairwise comparisons, who is the winner? A) A B) B = 3 pts C) C D) D E) None of the above.

7) Using the extended Borda Count ranking method, which candidate comes in last place? A) A = 82 B) B = 89 C) C =65 D) D = 74 E) None of the above.

8) Using the recursive plurality method, which candidate comes in second? A) A B) B C) C D) D E) None of the above. TIE between B + D (most correct answer) 9) Which of the candidates was the Majority candidate? A) A B) B C) C D) D E) None of the above.

10) Which of the candidates was the Condorcet candidate? A) A B) B C) C D) D E) None of the above. HONORS DISCRETE CHAPTER 1 REVIEW Election #1: Who is your favorite basketball player? 10 12 7 8 9 1st Jordan = 40 Lebron = 48 Kobe = 28 CP3 = 32 Lebron = 36 2nd CP3 = 30 Kobe = 36 CP3 = 21 Lebron = 24 Jordan = 27 3rd Lebron = 20 Jordan = 24 Jordan = 14 Jordan = 16 CP3 = 18 4th Kobe = 10 CP3 = 12 Lebron = 7 Kobe = 8 Kobe = 9 1) Determine the Winner of the Election using each voting method. Plurality = LEBRON Plurality with Elimination = CP3

Borda Count = LEBRON Pairwise Comparison = Tie Lebron, Kobe, CP3

2) Find each method’s EXTENDED RANKING for this election. Plurality Borda Count Plurality with Pairwise 1st = Lebron = 21 1st = Lebron = 135 Elimination Comparison 2nd = Jordan = 10 2nd = Jordan = 121 1st = CP3 1st = Lebron, 3rd = CP3 = 8 3rd = CP3 = 113 2nd = LEBRON Jordan, 4th = Kobe = 7 4th = Kobe = 91 3rd = JORDAN CP3 = 2 4th = KOBE 4th = KOBE

3) Check if there is a Majority or Condorcet candidate in the election. MAJORITY: NONE since no candidate has 24 or more 1st place votes

CONDORCET: NONE since no candidate wins all 3 match ups Lebron = 29 v. Jordan Lebron=49 v. Kobe Lebron v. CP3=25 Jordan=27 v. Kobe Jordan=27 v. CP3 Kobe v. CP3=27

4) Find the RECURSIVE RANKING for the election using plurality and plurality-with-elimination. Plurality Plurality with Elimination Round one: Lebron = 21 Round one: CP3 = 25 Round two: Jordan/ Kobe = 19 Round two: Lebron = 29 Round three: CP3 Round three: Jordan = 27 Round four: Kobe Election #2: What is your favorite type of music? 8 3 4 7 1st Rock = 32 Pop = 12 Hip-Hop = 12 Country = 28 2nd Country = 24 Rock = 9 Rock = 9 Rock = 21 3rd Hip-Hop = 16 Country = 6 Pop = 6 Pop = 14 4th Pop = 8 Hip-Hop = 3 Country = 3 Hip-Hop = 7 1) Determine the Winner of the Election using each voting method. 2) Find each method’s EXTENDED RANKING for this election. Plurality Borda Count Plurality with Pairwise Comparison 1st = Rock = 8 1st = Rock = 74 Elimination 1st = Rock = 3 2nd = Country = 10 2nd = Country = 62 1st = Rock 2nd = Country = 2 3rd = Hip Hop = 4 3rd = Hip Hop =42, 2nd = Country 3rd = Hip Hop = 1 4th = Pop = 3 Pop = 42 3rd = Hip Hop 4th = Pop =0 4th = Pop

3) Check if there is a Majority or Condorcet candidate in the election. MAJORITY: NONE since no candidate has 12 or more 1st place votes CONDORCET: Rock wins all 3 match ups

4) Find the RECURSIVE RANKING for the election using plurality and plurality- with-elimination. Plurality: Rock, Country, Hip Hop, Pop Plurality with Elimination: Rock, Country, Hip Hop, Pop

Election #3: What is your favorite type of movie? 8 3 4 6 1st Comedy = 32 Drama = 12 Comedy = 16 Drama = 24 2nd Drama = 24 Horror = 9 Drama = 12 Comedy = 18 3rd Horror = 16 Comedy = 6 Sci-Fi = 8 Sci-Fi = 12 4th Sci-Fi = 8 Sci-Fi = 3 Horror = 4 Horror = 6 1) Determine the Winner of the Election using each voting method. 2) Find each method’s EXTENDED RANKING for this election. Plurality Borda Count Plurality with Pairwise Comparison 1st = Comedy = 12 1st = Comedy, Elimination 1st = Comedy = 3 2nd = Drama = 10 Drama = 72 1st = Comedy 2nd = Drama = 2 3rd = Horror, 2nd = Horror = 35 2nd = Drama 3rd = Horror = 1 Sci Fi = 0 3rd = Sci Fi = 31 3rd = Horror, 4th = Sci Fi = 0 4th = Sci Fi

3) Check if there is a Majority or Condorcet candidate in the election. MAJORITY: COMEDY since it has 11or more 1st place votes CONDORCET: COMEDY wins all 3 match ups