Question 1

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

Accepted Answer

Peg 1st, J

Question 2

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

Accepted Answer

Lea 1st, S

Question 3

-According to the preference schedule from problem 9 , who is ranked second 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 4

-According to the preference schedule from problem 1, who is the winner of the election using the Borda Count 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

-The situations from problems (9) and (10) show an example of which of the Fairness Criterion being violated?

Accepted Answer

A)  Majority Criterion 
B)  Condorcet Criterion 
C)  Monotonicity Criterion 
D)  Independence of Irrelevant Alternatives Criterion 
E)  There is no criterion being violated. 
A)  Majority Criterion 
B)  Condorcet Criterion 
C)  Monotonicity Criterion 
D)  Independence of Irrelevant Alternatives Criterion 
E)  There is no criterion being violated.

Question 6

An election is held among five candidates (A, B, C, D, and E). There are 37 voters. Using the Method of Pairwise Comparisons it is found that  A, B , and  C  each win two pairwise comparison while  D  wins three. If  E  wins the remaining comparisons in this election, then which statement is true?

Accepted Answer

A)  D  is the Condorcet candidate. 
B)  E  is the Condorcet candidate. 
C)  D has a Majority of  1st  Choice Votes. 
D)  E has a Majority of  1st  Choice Votes. 
E)  None of the above is true. 
A)  D  is the Condorcet candidate. 
B)  E  is the Condorcet candidate. 
C)  D has a Majority of  1st  Choice Votes. 
D)  E has a Majority of  1st  Choice Votes. 
E)  None of the above is true.

Question 7

Find the smallest value of  X  so that a violation of the Condorcet Criterion occurs using the Plurality Method. Hint:  B  will be the winner using Plurality and  C  will be Condorcet.

Accepted Answer

The answer of Find the smallest value of  X...

Question 8

An election with four candidates (A, B, C, and D) and 150 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 smallest number of the remaining  30 1st  choice votes that  A must receive in order to guarantee a win?

Accepted Answer

A)  17 
B)  24 
C)  27 
D)  30 
E)  None of the above. 
A)  17 
B)  24 
C)  27 
D)  30 
E)  None of the above.

Question 9

-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 10

-According to the preference schedule from problem 1 , who is the winner of the election using the Borda Count 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

A new president is being chosen by your college's Math Club. The candidates are Alex (A), Betsy (B), Charlie  (C) , and Dana (D). The 27 members of the Math Club rank each candidate in order of preference and the results are tabulated below. Who would be chosen as the president of the Math Club using the Plurality with Elimination Method?

Accepted Answer

The answer of A new president is being chosen by...

Question 12

There are 280 voting members in your school's faculty union. Resort Alpha (A), Resort Beta (B), Resort Gamma (G) and Resort Delta (D) are the four possible resorts at which the union could hold its annual meeting. Each faculty member ranks the four resorts, and the Method of Plurality is being used to determine which resort will be chosen. Suppose that  30 %  of all members vote for Resort Alpha (A) as their  1st  choice. Assuming that all 280 members vote, then what is the smallest number of the remaining  1st  choice votes needed in order to guarantee that Resort Beta (B) is the winner?

Accepted Answer

Question 13

As of 2012 , there are 435 voting members in the US House of Representatives. At the opening session of the House, it is customary to have each Representative shake hands once with every other Representative. How many handshakes would this account for in 2012?

Accepted Answer

A)  870 
B)  94395 
C)  94830 
D)  189225 
E)  None of the above. 
A)  870 
B)  94395 
C)  94830 
D)  189225 
E)  None of the above.

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

Independen

Question 16

An election consists of four candidates  A, B, C , and  D . The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below.
How many votes are required in order to obtain a majority of votes?

Accepted Answer

A)  18 
B)  27 
C)  36 
D)  71 
E)  None of the above. 
A)  18 
B)  27 
C)  36 
D)  71 
E)  None of the above.

Question 17

Using the Plurality with Elimination Method, rank the contestants from the following election.

Accepted Answer

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

Question 18

-According to 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 19

The Board of Trustees at your college is holding elections to determine which candidate from the faculty will be chosen to head up the new Committee on Voting Standards. The choices are Dr. Abel, Dr. Barnes, Dr. Corza, and Dr. Davis or A, B, C, and D, respectively. The trustees have ranked the candidates from their first choice to their fourth choice, and the results are given below in the preference table.
 
Who will be chosen as the candidate to head up the Committee on Voting Standards if the trustees use the Plurality with Elimination Method?

Accepted Answer

The answer of The Board of Trustees at your college...

Question 20

-Use the scenario and preference schedule from problem 7. Suppose that Dr. Davis (D) has to withdraw her name from consideration. Remove D from the preference table and shift all votes up one slot. Who will be chosen as the candidate to head up the Committee on Voting Standards, if the trustees use the Plurality with Elimination Method with the new preference table?

Accepted Answer

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

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

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

-According to the preference schedule from problem 9 , who is ranked second using the Borda Count Method?

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

-The situations from problems (9) and (10) show an example of which of the Fairness Criterion being violated?

An election is held among five candidates (A, B, C, D, and E). There are 37 voters. Using the Method of Pairwise Comparisons it is found that A, B , and C each win two pairwise comparison while D wins three. If E wins the remaining comparisons in this election, then which statement is true?

Find the smallest value of X so that a violation of the Condorcet Criterion occurs using the Plurality Method. Hint: B will be the winner using Plurality and C will be Condorcet.

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

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

As of 2012 , there are 435 voting members in the US House of Representatives. At the opening session of the House, it is customary to have each Representative shake hands once with every other Representative. How many handshakes would this account for in 2012?

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

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

An election consists of four candidates A, B, C , and D . The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below. How many votes are required in order to obtain a majority of votes?

Using the Plurality with Elimination Method, rank the contestants from the following election.

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

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

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

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

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

-According to the preference schedule from problem 9 , who is ranked second using the Borda Count Method?

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

-The situations from problems (9) and (10) show an example of which of the Fairness Criterion being violated?

An election is held among five candidates (A, B, C, D, and E). There are 37 voters. Using the Method of Pairwise Comparisons it is found that A, B , and C each win two pairwise comparison while D wins three. If E wins the remaining comparisons in this election, then which statement is true?

Find the smallest value of X so that a violation of the Condorcet Criterion occurs using the Plurality Method. Hint: B will be the winner using Plurality and C will be Condorcet.

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

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

As of 2012 , there are 435 voting members in the US House of Representatives. At the opening session of the House, it is customary to have each Representative shake hands once with every other Representative. How many handshakes would this account for in 2012?

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

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

An election consists of four candidates A, B, C , and D . The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below. How many votes are required in order to obtain a majority of votes?

Using the Plurality with Elimination Method, rank the contestants from the following election.

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

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