pairwise comparisons, math homework help

User Generated

juvgarlwbv

Mathematics

Description

For Halloween, a group of students were asked to vote for their favorite horror movies. Their choices were Alien, The Blair Witch Project, The Conjuring, and Dreamcatcher (A, B, C, D for short). The following table gives the preference schedule for the election.

Number of Voters

17

14

12

8

7

1st Choice

C

A

B

D

B

2nd Choice

D

B

D

A

D

3rd Choice

B

C

C

C

A

4th Choice

A

D

A

B

C

1.Use the pairwise-comparisons method to find the winner of the election. Show work

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Explanation & Answer

For the pairwise-comparison method, let's consider all the possible head-to-head combinations for these 4 choices. For simplicity, let's call the columns of ranked vote choices by roman numerals I-V (i.e., I represents the 17 votes with C-D-B-A from 1st to 4th, whereas II represents the 14 votes with A-B-C-D). For each head-to-head combination, we give the votes from each column I-V to whichever head-to-head competitor is higher in the ranking. The possible head-to-head combinations are:A vs. B. In this case, A gets the votes in II and IV, whereas B gets the votes in I, III, and V. Thus, there are 14+8=22 votes for A and 17+12+7=36 votes for B. B wins 36-22.A vs. C. In this case, A gets the votes in II, IV and V, whereas C gets the votes in I and III. Thus, there are 14+8+7=29 votes for A and 17+12=29 votes for C. A and C tie 29-29.A vs. D. In this case, A gets the votes in II, whereas D gets the votes in I, III, IV, and V. Thus, there are 14 votes f...


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