Here is the preference schedule for a recent election among four candidates: Number of voters 1 4 7 23 11 5 10 1st choice X X F F B F K 2nd choice K F X B K K X 3rd choice B K B X F X B 4th choice F B K K X B F How many voters voted in this election?  How many first place votes are needed for a majority?  Which candidate/choice had the most first-place votes?  Which candidate/choice has the least first-place votes?  Which candidate/choice had the most last-place votes?  Which candidate/choice has the least last-place votes?    Question 6 :    Number of voters 21 21 10 34 38 16 1st choice C D B A C A 2nd choice B A C B A D 3rd choice A B A D B B 4th choice D C D C D C Find the winner of the election using the Pairwise Comparison method. For each comparison, enter the number of times each candidate was preferred to the other. A vs. B Votes where A is preferred to B :  Votes where B is preferred to A :  A vs. C Votes where A is preferred to C :  Votes where C is preferred to A :  A vs. D Votes where A is preferred to D :  Votes where D is preferred to A :  B vs. C Votes where B is preferred to C :  Votes where C is preferred to B :  B vs. D Votes where B is preferred to D :  Votes where D is preferred to B :  C vs. D Votes where C is preferred to D :  Votes where D is preferred to C :  Tally the results: Points for A:  Points for B:  Points for C:  Points for D:  Who is the winner? A B C D There is a tie Answer both please.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 40E: Choosing Officers From a pool of 12 candidates, the offices of president, vice-president, secretary,...
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Here is the preference schedule for a recent election among four candidates:

Number of voters 1 4 7 23 11 5 10
1st choice X X F F B F K
2nd choice K F X B K K X
3rd choice B K B X F X B
4th choice F B K K X B F



How many voters voted in this election? 

How many first place votes are needed for a majority? 

Which candidate/choice had the most first-place votes? 

Which candidate/choice has the least first-place votes? 

Which candidate/choice had the most last-place votes? 

Which candidate/choice has the least last-place votes? 

 

Question 6 : 

 

Number of voters 21 21 10 34 38 16
1st choice C D B A C A
2nd choice B A C B A D
3rd choice A B A D B B
4th choice D C D C D C



Find the winner of the election using the Pairwise Comparison method. For each comparison, enter the number of times each candidate was preferred to the other.

A vs. B
Votes where A is preferred to B : 
Votes where B is preferred to A : 

A vs. C
Votes where A is preferred to C : 
Votes where C is preferred to A : 

A vs. D
Votes where A is preferred to D : 
Votes where D is preferred to A : 

B vs. C
Votes where B is preferred to C : 
Votes where C is preferred to B : 

B vs. D
Votes where B is preferred to D : 
Votes where D is preferred to B : 

C vs. D
Votes where C is preferred to D : 
Votes where D is preferred to C : 

Tally the results:
Points for A: 
Points for B: 
Points for C: 
Points for D: 
Who is the winner?

  • A
  • B
  • C
  • D
  • There is a tie

Answer both please.

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