PLEASE COMPLETE THESE ON MICROSOFT WORD . show workings Step by step

19.The Adobe School District is hiring a vice principal and has interviewed four candidates: Andrew (A), Bono (B), Carol (C), and Davy (D). The hiring committee members have indicated their preferences:

(ACDB)(CBAD)(BCDA)(DBCA)

7 5 3 2

• a.Who is the winner using the plurality method?
• b.Suppose that Carol drops out of the running before the vote is taken. Who is the winner using the plurality method?

25.The seniors at Weseltown High School are voting for where to go for their senior trip. They are deciding on Angel Falls (A), Bend Canyon (B), Cedar Lake (C), or Danger Gap (D). The results of the preferences are:

(DABC)(ACBD)(BCAD)(CBDA)(CBAD)

80 45 30 10 50

A.Who is the Condorcet candidate?

B.Is there a majority winner? If not, is there a plurality winner? Does this violate the Condorcet criterion?

C.Is there a majority winner? If not, is there a plurality winner? Does this violate the Condorcet criterion?

D.Who wins using the Hare method? Does this violate the Condorcet criterion?

42.A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are:

(ABC)(CBA)(BCA)

6 5 4

• a.Is there a Condorcet candidate?
• b.Is there a majority? If not, who wins the plurality vote? Does this violate the Condorcet criterion?

c.Who wins using the Borda count method? Does this violate the Condorcet criterion?

d.Who wins the election using the Hare method? Does this violate the Condorcet criterion?

46.The fraternity

is electing a national president, and there are four candidates: Alberto (A), Bate (B), Carl (C), and Dave (D). The voter preferences are:

(BDCA)(BDAC)(CDAB)(ADCB)

100 120 130 150

• a.How many votes were cast?
• b.Is there a majority? If not, who wins the plurality vote?
• c.Is there a Condorcet candidate?

55.Consider an election with three candidates with the following results:

(ACB)(BAC)(CBA)(CAB)

2 5 4 2

• a.Is there a majority winner? If not, who is the plurality winner?
• b.Who wins the election using the Borda count method?
• c. Who wins if he or she first eliminates the one with the most last-place votes and then has a runoff between the other two?
• d.Could the two voters with preference (CAB) change the outcome of the election inpart cif they voted insincerely and pretended to have the preference (CBA)?