Question 1

-According to the preference schedule from problem 1, which candidate, if any, will receive a majority
of 5th choice votes?

Accepted Answer

Joe

Question 2

-According to the preference schedule from problem 1, Sam would be voted the next Campus Idol using the Plurality Method. Would this result be a violation of the Condorcet Criterion? Explain.

Accepted Answer

Yes, because Frank is the Condorcet
candidate and thus should be the
winner.

Question 3

-According to the preference schedule from problem 1, rank the five students using the Plurality Method.

Accepted Answer

Peg 1st, Lea 2nd, Joe 3rd, Sam 4th, Val
5th

Question 4

-According to the preference schedule from problem 1, who is the winner of the election using the Plurality Method?

Accepted Answer

A)  A 
B)  B 
C)  C 
D)  D 
E)  There is a tie. 
A)  A 
B)  B 
C)  C 
D)  D 
E)  There is a tie.

Question 5

-Which Fairness Criterion is being violated by the actions shown in problems 7 and 8?

Accepted Answer

Independen

Question 6

Five students are taking part in the Campus Talent Show. Each of the five students will perform their talent in front of an audience and once all the performers have finished the audience members will rank each participant in order of preference. The candidate who has the highest ranking will move on to the national competition. The final preference schedule is given below.
 
Rank the five students using the Borda Count Method.

Accepted Answer

Lea 1st, S

Question 7

An election with four candidates (A, B, C, and D) and 180 voters will use the Plurality Method to choose a winner. After 120 ballots have been recorded, A has  26 1st  choice votes, B has  18 1st  choice votes, C has  42 1st choice votes, and D has  34 1st  choice votes. What is the minimum number of the remaining  60 1st  choice votes that  A  must receive in order to guarantee that no candidate will receive a majority of  1st choice votes?

Accepted Answer

A)  12 
B)  15 
C)  16 
D)  24 
E)  None of the above. 
A)  12 
B)  15 
C)  16 
D)  24 
E)  None of the above.

Question 8

-Using the preference schedule from problem 1 , who is the winner of the election using the Method of Pairwise Comparisons?

Accepted Answer

A)  A 
B)  B 
C)  C 
D)  D 
E)  There is a tie. 
A)  A 
B)  B 
C)  C 
D)  D 
E)  There is a tie.

Question 9

Using the Borda Count Method, rank the contestants from the following election.

Accepted Answer

A)  Ali  1st , Deb  2nd , Cat  3rd , Bob  4th 
B)  Cat  1st , Ali  2nd , Deb  3rd , Bob  4th 
C)  Ali  1st , Cat  2nd , Deb  3rd , Bob  4th 
D)  Deb  1st , Bob  2nd , Ali  3rd , Cat  4th 
E)  None of the above. 
A)  Ali  1st , Deb  2nd , Cat  3rd , Bob  4th 
B)  Cat  1st , Ali  2nd , Deb  3rd , Bob  4th 
C)  Ali  1st , Cat  2nd , Deb  3rd , Bob  4th 
D)  Deb  1st , Bob  2nd , Ali  3rd , Cat  4th 
E)  None of the above.

Question 10

-Using the preference schedule from problem 1 , who is the winner of the election using the Plurality with Elimination Method?

Accepted Answer

A)  A 
B)  B 
C)  C 
D)  D 
E)  There is a tie. 
A)  A 
B)  B 
C)  C 
D)  D 
E)  There is a tie.

Question 11

The Plurality with Elimination method can possibly violate which of the Fairness Criteria?

Accepted Answer

A)  Condorcet Criterion 
B)  Monotonicity Criterion 
C)  Independence of Irrelevant Alternatives Criterion 
D)  Majority Criterion 
E)  (a), (b) and (c) 
A)  Condorcet Criterion 
B)  Monotonicity Criterion 
C)  Independence of Irrelevant Alternatives Criterion 
D)  Majority Criterion 
E)  (a), (b) and (c)

Question 12

An election consists of four candidates  A , B , C , D  .  The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below.
 
Which candidate, if any, received a majority of  1st  choice votes?

Accepted Answer

A)  A 
B)  B 
C)  C 
D)  D 
E)  None of the above. 
A)  A 
B)  B 
C)  C 
D)  D 
E)  None of the above.

Question 13

Since 2011, a total of 68 college basketball teams quality for the NCAA March Madness Tournament. These teams play each other in a series of games in a bracket style competition resulting in a total of 67 games. However, suppose that each team was required to play one game against everyone other participating team in a round-robin style tournament. How many games would this entail?

Accepted Answer

The answer of Since 2011, a total of 68 college...

Question 14

-According to the preference schedule from problem 1, who would be the next Campus Idol if the Borda Count Method was used to choose the winner?

Accepted Answer

The answer of  
-According to the preference schedule from...

Question 15

-According to the preference schedule from problem 1, who is the winner of the election using the Method of Pairwise Comparisons?

Accepted Answer

A)   A 
B)  B 
C)  C 
D)  D 
E)  There is a tie. 
A)   A 
B)  B 
C)  C 
D)  D 
E)  There is a tie.

Question 16

Your college radio station is holding auditions to find the next Campus Idol. There are four people competing in the auditions: Beth (B), Frank (F), Helen (H), and Sam (S). After all of the competitors have auditioned, the audience members rank each contestant in order of preference and submit their ballots. The results are given below.
 
How many preference ballots were cast in this competition?

Accepted Answer

The answer of Your college radio station is holding auditions...

Question 17

-According to the preference schedule from problem 9 , if Cat drops out of the race and all votes shift up one slot, then who will win the race using the Borda Count Method?

Accepted Answer

A)  Ali 
B)  Bob 
C)  Cat 
D)  Deb 
E)  None of the above. 
A)  Ali 
B)  Bob 
C)  Cat 
D)  Deb 
E)  None of the above.

Question 18

The Student Government at your college consists of 184 voting members. A motion regarding funding
for a new club activity is brought to the floor. The four possible activities for which a member could
vote are the Karaoke Club (K), Hiking Club (H), Jousting Club (J) and Dog-Lovers Club (D). If the
Karaoke Club (K) receives a total of 48 votes, then what is the minimum number of votes needed by
one of the remaining clubs to ensure that no club can receive a majority of all votes?

Accepted Answer

The answer of The Student Government at your college consists...

Question 19

Which of the four Voting Methods (Plurality, Borda Count, Plurality with Elimination or Pairwise Comparison) will never violate the Majority Criterion and the Condorcet Criterion?

Accepted Answer

The answer of Which of the four Voting Methods (Plurality,...

Question 20

-Use the scenario and preference schedule from problem 7. Suppose that Dana is asked to be president of the Latin Club and has to withdraw from the race before the results are made public. Realign the preference table by removing D and shifting all of the votes up one slot. Now who would be chosen as the president of the Math Club using the Plurality with Elimination Method?

Accepted Answer

The answer of  
-Use the scenario and preference schedule...

-According to the preference schedule from problem 1, which candidate, if any, will receive a majority of 5th choice votes?

-According to the preference schedule from problem 1, Sam would be voted the next Campus Idol using the Plurality Method. Would this result be a violation of the Condorcet Criterion? Explain.

-According to the preference schedule from problem 1, rank the five students using the Plurality Method.

-According to the preference schedule from problem 1, who is the winner of the election using the Plurality Method?

-Which Fairness Criterion is being violated by the actions shown in problems 7 and 8?

-Using the preference schedule from problem 1 , who is the winner of the election using the Method of Pairwise Comparisons?

Using the Borda Count Method, rank the contestants from the following election.

-Using the preference schedule from problem 1 , who is the winner of the election using the Plurality with Elimination Method?

The Plurality with Elimination method can possibly violate which of the Fairness Criteria?

An election consists of four candidates A , B , C , D . The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below. Which candidate, if any, received a majority of 1^st choice votes?

-According to the preference schedule from problem 1, who would be the next Campus Idol if the Borda Count Method was used to choose the winner?

-According to the preference schedule from problem 1, who is the winner of the election using the Method of Pairwise Comparisons?

-According to the preference schedule from problem 9 , if Cat drops out of the race and all votes shift up one slot, then who will win the race using the Borda Count Method?

Which of the four Voting Methods (Plurality, Borda Count, Plurality with Elimination or Pairwise Comparison) will never violate the Majority Criterion and the Condorcet Criterion?

The Mathematics of Power: Weighted Voting

The Mathematics of Sharing: Fair-Division Games

The Mathematics of Apportionment: Making the Rounds

The Mathematics of Getting Around: Euler Paths and Circuits

The Mathematics of Touring: Traveling Salesman Problems

The Cost of Being Connected

The Mathematics of Scheduling: Chasing the Critical Path

Population Growth Models: There Is Strength in Numbers

Financial Mathematics: Money Matters

The Mathematics of Symmetry: Beyond Reflection

Fractal Geometry: the Kinky Nature of Nature

Fibonacci Numbers and the Golden Ratio: Tales of Rabbits and Gnomons

Censuses, Surveys, Polls, and Studies: the Joys of Collecting Data

Graphs, Charts, and Numbers: the Data Show and Tell

Probabilities, Odds, and Expectations: Measuring Uncertainty and Risk

The Mathematics of Normality: the Call of the Bell

Filters

Exam 1: The Mathematics of Elections: the Paradoxes of Democracy

-According to the preference schedule from problem 1, which candidate, if any, will receive a majority of 5th choice votes?

-According to the preference schedule from problem 1, Sam would be voted the next Campus Idol using the Plurality Method. Would this result be a violation of the Condorcet Criterion? Explain.

-According to the preference schedule from problem 1, rank the five students using the Plurality Method.

-According to the preference schedule from problem 1, who is the winner of the election using the Plurality Method?

-Which Fairness Criterion is being violated by the actions shown in problems 7 and 8?

-Using the preference schedule from problem 1 , who is the winner of the election using the Method of Pairwise Comparisons?

Using the Borda Count Method, rank the contestants from the following election.

-Using the preference schedule from problem 1 , who is the winner of the election using the Plurality with Elimination Method?

The Plurality with Elimination method can possibly violate which of the Fairness Criteria?

An election consists of four candidates A , B , C , D . The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below. Which candidate, if any, received a majority of 1st choice votes?

-According to the preference schedule from problem 1, who would be the next Campus Idol if the Borda Count Method was used to choose the winner?

-According to the preference schedule from problem 1, who is the winner of the election using the Method of Pairwise Comparisons?

-According to the preference schedule from problem 9 , if Cat drops out of the race and all votes shift up one slot, then who will win the race using the Borda Count Method?

Which of the four Voting Methods (Plurality, Borda Count, Plurality with Elimination or Pairwise Comparison) will never violate the Majority Criterion and the Condorcet Criterion?

The Mathematics of Power: Weighted Voting

The Mathematics of Sharing: Fair-Division Games

The Mathematics of Apportionment: Making the Rounds

The Mathematics of Getting Around: Euler Paths and Circuits

The Mathematics of Touring: Traveling Salesman Problems

The Cost of Being Connected

The Mathematics of Scheduling: Chasing the Critical Path

Population Growth Models: There Is Strength in Numbers

Financial Mathematics: Money Matters

The Mathematics of Symmetry: Beyond Reflection

Fractal Geometry: the Kinky Nature of Nature

Fibonacci Numbers and the Golden Ratio: Tales of Rabbits and Gnomons

Censuses, Surveys, Polls, and Studies: the Joys of Collecting Data

Graphs, Charts, and Numbers: the Data Show and Tell

Probabilities, Odds, and Expectations: Measuring Uncertainty and Risk

The Mathematics of Normality: the Call of the Bell

Filters

An election consists of four candidates A , B , C , D . The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below. Which candidate, if any, received a majority of 1^st choice votes?