Reference no: EM132376228
An election was held using the following variation of the Borda count method: 7 points for first place, 4 points for second, 3 points for third, 2 points for fourth, and 1 point for fifth. There were five candidates (A, B, C, D, and E) and 50 voters. When the points were tallied, A had 152 points, B had 133 points, C had 191 points, and D had 175 points. Find out how many points E had and give the ranking of the candidates.
Below you are given a preference schedule for an election with five candidates. Use the plurality with elimination method to find the complete ranking of the candidates.
Number of Voters
10 9 9 5 4 2
1st C B B A C B
2nd D D D C B C
3rd A C A D D D
4th B A C B A A
Consider the weighted voting system [q: 10, 8, 6, 4, 2]. Find the smallest value of q for which All five players have veto power. Explain.
P3 has veto power but P4 does not. Explain.
The Jones family has two parents and three children. Family vacations are decided by a majority of the total votes, but at least one parent must vote yes. If we use [q: p, p, c, c, c] to describe this weighted voting system, find values for q, p, and c. Explain and show your process for how you arrived at your answer and then verify that the requirements in sentence 2 are met. Show your work. (There are many correct answers to this problem.)
Consider the weighted voting system [9: w, 5, 2, 1].
What are the possible values of w? Explain.
Which values of w result in a dictator? Who is the dictator? How do you know this person a dictator?
Which values of w result in a player with veto power? Who has veto power? Why?
Which values of w result in one or more dummies? Who is the dummy? Why?
In the weighted voting system [q : 24, 12, 8, 4, 2], what is the smallest possible value of the quota q for which
P_5 is a dummy.
P_4 and P_5 are both dummies.
Three friends were at an auction. For $14,900, they bought a bag guaranteed to contain 36 high quality pearls. Alice contributed $5900, Bob's contribution was $7600, and Charlie supplied the remaining $1400.
They take the bag home and pour the 36 pearls onto the table. Use Hamilton's method to determine how many pearls each person should receive based on the financial contribution.
Charlie notices the bag isn't empty! Another pearl comes out. Recalculate the apportionment based on the new number of pearls. (You are still using Hamilton's method.)
What do you notice about the apportionment in part b? Does it seem fair based on your result from part a? Which violation or paradox is this example demonstrating? Explain.
A university made up of 5 schools: Liberal Arts, Natural Sciences, Performing Arts, Business, and Engineering has 250 new computers to distribute among the 5 schools based on the enrollment.
School Liberal Arts Natural Sciences Performing Arts Business Engineering
Enrollment 7095 2131 937 1091 1746
Apportion the computers using Hamilton's method.
Apportion the computers using Jefferson's Method. (HINT: You will need to use a decimal in your modified divisor)
Compare the apportionments from parts a and b. Note any differences in apportionment and which schools were favored by the different methods.
A small country composed of states must apportion 70 representatives.
State A B C D E
Population 300,500 200,000 50,000 38,000 21,500
Determine the distribution of the trucks using Webster's Method.
Determine the distribution of the trucks using the Huntington-Hill Method.
Compare the apportionments from parts a and b.
Do any violations or paradoxes occur? Explain.