mgf1107ans1

# mgf1107ans1 - MGF 1107 TEST ONE REVIEW-SOLUTIONS TO THE...

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MGF 1107 TEST ONE REVIEW-SOLUTIONS TO THE SHOW WORK PROBLEMS A wealthy anonymous donor decided to give a certain city \$1,000,000. The only condition is that the money is all used for a single project. The choices are road construction, re-vitalizing the downtown area, building a new auditorium, and increasing police officer salaries. A volunteer committee of 36 residents were formed to vote on the project and the results yielded the preference lists given below: (R = road construction, D = downtown re-vitalization, A = building the auditorium, and P = increasing police officer salaries.) 14 10 7 5 First R A D P Second A D P D Third D P A A Fourth P R R R Find the winner of the election using: 1) Plurality with Runoff The candidates with the first and second most first places votes are R (14) and A (10). In the runoff, we have A over R by 22 to 14. 2) The Hare System Stage One: Omit P 14 10 7 5 First R A D Second A D D Third D A A Fourth R R R Stage Two: Omit A (D now has 12 first place votes to A’s 10) 14 10 7 5 First R D D Second D Third D Fourth R R R Stage Three: D emerges as the winner over R by 22 to 14. 3) The Borda Count 14 10 7 5 First R A D P Second A D P D Third D P A A Fourth P R R R

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Assign 0 points for 4 th , 1 point for 3rd, 2 points for 2 nd , and 3 points for 1 st . Borda Score for R: (3)(14)+ (0)(10)+ (0)(6) + (0)(5) = 42 + 0 + 0 + 0 = 42 Borda Score for A: (2)(14) + (3)(10) + (1)(7) + (1)(5) = 28 + 30 + 7 +5 = 70 Borda Score for D: (1)(14) + (2)(10) + (3)(7) + (2)(5) = 14 + 20 + 21 + 10 = 65 Borda Score for P: (0)(14) + (1)(10) + (2)(7) + (3)(5) = 0 + 10 + 14 + 15 = 39 A wins using the Borda Count. 4) Sequential Pairwise Voting with the agenda D,A,R,P D to A: 12 to 24.-A wins A to R: 22 to 14- A wins A to P: 24 to 12-A wins using Sequential Pair-wise Voting the agenda D,A,R,P. An election was held to decide on a county project committee leader for Pima County, AZ. There were five candidates to choose from, Ms. Adams, Ms. Barnes, Mr. Cole, Mr. Diaz, and Dr. Elliot. The 10 people voting determined the following preference lists: 3 2 1 1 1 1 1 First A D E E E B C S e c o n dCCDBCCB Third E B B A D E D F o u r t h DACCBDA F i f t h BE ADAAE 5) Plurality with Runoff A and E tie for the most first place votes and D has the second most. We will have a runoff with the three
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mgf1107ans1 - MGF 1107 TEST ONE REVIEW-SOLUTIONS TO THE...

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