1. 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? Answer A wins

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

2. 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) 30 25 22 20 11

i.Who is the Condorcet candidate? Answer A is the Condorcet candidate.

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

iii. Who wins the Borda count? Does this violate the Condorcet criterion? Answer A wins; no

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

3.A group of fun-loving people have decided to play a practical joke on one of their friends, but they cant decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (ABC) (CBA) (BCA) 6 5 4

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

ii. Who wins using the Borda count method? Does this violate the Condorcet criterion? Answer Betty wins; no

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

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

BDCA BDAC CDAB ADCB

100 120 130 150

i. a. How many votes were cast?

b. Is there a majority? If not, who wins the plurality vote?

c. Is there a Condorcet candidate

ii.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? Answer no majority; C wins plurality

b. Who wins the election using the Borda count method? Answer There is no winner because B and C tie