Discrete Math Project

What is a preference ballot? (1.1)

• A letter of reccomendation

• A ballot in which voters are asked to rank candidates in order of preference

• The input/output of ballots

• A logical way to organize the ballots by grouping identical ones together

An election with 4 candidates (A,B,C,D) and 150 voters is to be decided using the plurality method. After 120 ballots have been recorded, A has 26 vote, B has 18 votes, C has 42 votes, and D has 34 votes.

For A to win the election outright using the Plurality Method, at least how many of the remaining 30 votes need to have C in first place? (1.2)

• 24

• 7

• 23

• 16

Use the Borda Count Method to find the winner of the election. (1.3)

• The winner is D

• The winner is C

• The winner is A

• The winner is B

What criterion/rule does the Plurality-With-Elimination method violate? (1.4)

• The Multiplication Rule

• The Independence-Of-Irrelevant-Alternatives Criterion

• The Monotonicity Criterion

• The Quota Rule

An election with 5 candidates (A,B,C,D,E) is decided using the method of Pairwise Comparisons. Suppose that B loses 2 pairwise comparisons, C loses 1, D loses 1 and ties 1, and E loses 2 and ties 1.

Who was the winner of the election? (1.5)

• The winner is B

• The winner is C

• The winner is A

• The winner is D

In an election with 3 candidates, what is the maximum number of columns possible in the preference schedule?

• 4

• 3

• 10

• 6

Which player is a dictator in this set?

[15:16,8,4,1]

• p2

• p1

• p3

• p4

What is the weight of the coalition formed by p1 and p3?

[10:6,5,4,2]

• 10

• 9

• 8

• 12

Find the Shapley-Shubik power distribution of each of the following weighted voting system.

[15:16,8,4,1]

• p1-1/2 p2-1/4 p3-1/4 p4-0

• p1-0 p2-1 p3-0 p4-0

• p1-1 p2-0 p3-0 p4-0

• p1-1/4 p2-1/4 p3-1/4 p4-1/4

Determine which of these players are dummies in this set

[18:16,8,4,1]

• p3,p4

• p2,p3

• p1

• p4