Determine which candidate would have won if all of the

Question

QUESTION 1

Answer the following questions based on the preference schedule to the right for an election decided with the Plurality method:

	2	5	8	9
1st	C	A	C	D
2nd	B	D	A	B
3rd	A	B	D	A
4th	D	C	B	C

a. Determine the winner of the election.

b. Determine whether or not there was a Condorcet candidate in this election.

c. Does this election demonstrate a violation of the Condorcet criterion?

d. Determine which candidate would have won if all of the preference ballots had been reversed.

e. Does this election illustrate a violation of the reversal criterion?

QUESTION 2

Answer the following questions based on the preference schedule to the right for an election decided with the Borda Count method:

	9	4	5	4	6
1st	A	C	D	B	D
2nd	C	A	B	A	A
3rd	D	B	A	C	C
4th	B	D	C	D	B

a. Determine the winner of the election. (Show point totals for each player.)

b. Explain whether or not there was a Majority candidate in this election.

c. Does this election demonstrate a violation of the Majority criterion?

d. Determine whether or not there was an Anti­ Condorcet candidate in this election.

e. Does this election demonstrate a violation of the anti­Condorcet criterion?

QUESTION 3

Answer the following questions based on the preference schedule to the right for an election decided with the Copeland's method:

	7	5	13	15
1st	A	B	C	D
2nd	D	A	A	B
3rd	B	C	B	C
4th	C	D	D	A

a. Determine the winner of the election.

b. Determine whether or not there was a Condorcet candidate in this election.

c. Does this election demonstrate a violation of the Condorcet criterion?

d. Which candidate would have won if C had not been in the election?

e. Does having C drop out of the election demonstrate a violation of the Irrelevant Alternative criterion?

QUESTION 4

Answer the following questions based on the preference schedule to the right for an election decided with the Instant Runoff Voting method:

	11	4	9	3	10
1st	D	C	A	C	B
2nd	A	B	B	A	C
3rd	B	D	D	D	D
4th	C	A	C	B	A

a. Determine the winner of the election.

b. Determine which candidate would have won if all of the preference ballots had been reversed.

c. Does this election demonstrate a violation of the Reversal Criterion?

d. Suppose that 5 additional ballots were included that had C 1st, A 2nd, D 3rd, and B 4th. Explain which candidate would have won.

e. Do the inclusion of the additional ballots in part (d) demonstrate a violation of the Participation criterion?

QUESTION 5

An election is held with 5 candidates and 200 voters and is decided using the plurality method. The most first place votes a candidate could receive but still lose is.

QUESTION 6

Larry, Curly and Moe all ran for Head Mucky­Muck at Band Camp. The campers voted by writing out their preference ballots on a piece of paper and then handing them to the camp counselor. The counselor counted the votes, performed the voting method and found that Larry would win. Just to make sure she counted the votes again. While doing this she found that she had missed two votes that had Larry in first place. So she performed the voting method again with Larry starting with two more 1st place votes. This time she found that Moe won.

a) Explain which fairness criterion violation is illustrated in this example.

b) Based on your answer to part a) which voting method or methods (plurality, Copeland's, Instant Runoff, Borda count) could the teacher have been using?

QUESTION 7

At the beginning of the semester your math teacher said to the class "If you do all your homework then I guarantee you will pass the class." Your friend Jonas passed the class. Based on this, what do you know about whether or not Jonas did all his homework?

QUESTION 8

Determine the winner of the following election using either the Bucklin's method, Coombs method, or Black's method (See the exercises in the book to find the description for these). Clearly denote which method you are using and show your work.

	7	10	6	5	6
1st	A	B	A	C	C
2nd	D	D	D	A	B
3rd	C	A	B	B	D
4th	B	C	C	D	A