Number of voters141411119I. Head-to-head total score:X:vs. Y:II. Head-to-head total score:X:vs. Z:III. Head-to-head total score:Y:vs. Z:PreferenceY>Z> XX>Y > ZZ>X > YZ>Y > XX>Z> Y

Answered: Number of voters 14 14 11 11 9 I.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Number of votes 5 3 4 1st O L e 2nd l e l 3rd e o o determine the winner using the pairwise comparison method
1. Using the method of Pairwise comparison, who is the winner? 2. Using the Borda count method, which candidate comes in second?
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First Profile # of Voters C>D>B>A A>B>D>C Second Profile Ranking #of Ranking A 22-member committee is selecting a site for its next meeting. The choices are City A, City B, City C, and City D. Voters 7 C>D>B>A A>B>D>C A>B>C>D C>A>D>8 6. 5 A>B>C>D 5 4 D>C>B>A 4 (a) The committee members decide to use the pairwise comparison method to select a site in a nonbinding decision. Prior to any discussion, the 22 members rank the choices according to the first voter profile above. Show that City C is selected by the pairwise comparison method in the preliminary nonbinding decision. Complete the table below to demonstrate this. City A. Pairwise Comparison Points O (Type integers or decimals.) (b) The 4 committee members with the bottom ranking in the table rearrange their ranking after listening to the discussions. The other 18 committee members stick with their original rankings of the cities. For the official vote, the 22 members rank the choices according to the second voter profile above.…
1. List the total points for each candidate. Show how you calculate each candidate's total points. A: 160+100+30+18-308 B: 120+75+60+54=309 C: 80+25+120+72=297 D: 40+50+90+36-216 2. Under the Borda method, the candidate who wins the vote is B 3. How many votes are needed to win the majority? 566 votes are needed to win the majority. 4. Now determine the head-to-head winner. Fill in the table below. The first column is filled out for you as an example. 40 25 30 18 Winner in Head-to-Head A vs B A vs C A vs D A-40 A-25 B-30 B-18 B vs C B vs C C vs D 5. Who wins the head-to-head? How does the candidate win the head-to-head? 6. What can you say about the head-to-head criterion? Determine whether or not the Borda method violates the head-to-head criterion. Write your response below:
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Number of voters 14 14 11 11 9 I. Head-to-head total score: X: vs. Y: II. Head-to-head total score: X: vs. Z: III. Head-to-head total score: Y: vs. Z: Preference Y>Z> X X>Y > Z Z>X > Y Z>Y > X X>Z> Y