Fair Division and Apportionment Project
Part 1: Distributing Flights for United Pacific Airlines
United Pacific, a start-up airline company, has created the new TrainPlane! They will start with
sixty-five flights per month on three routes. Those routes are: Chicago to New York, Chicago to
Los Angeles, and Chicago to Miami. They anticipate 4010 passengers flying from Chicago to
New York, 3150 flying from Chicago to Los Angeles, and 1840 flying from Chicago to
Miami. Apportion the flights to the routes based on the number of anticipated passengers using
the Hamilton Method and Jefferson Method. Make sure to show all work and write a conclusion
statement discussing the final apportionment. Round to four decimal places for all values when
showing work.
Part 2: Distributing Union Seats
The Board of Directors of a Union for a trucking company has allotted 12 seats for liaisons of its
three divisions. One division, Local 28 (better known as the Teamsters) consists of the drivers.
There are 60 employees in the Local 28 division. The second division, Local 17, consists of
office employees. There are 10 employees in Local 17. The third division, Local 5, consists of
the casuals, non-drivers, and dock workers. There are 35 employees in Local 5. Use the
Huntington- Hill method to apportion the seats. Write a short conclusion discussing your
findings.
a) Do you feel your method results in the fairest division of seats? Why or why not? What makes
the division fair?
Part 3: Scheduling Math Classes
Downtown Utopian High is a small, private, high school has only one mathematics teacher who
teaches five classes each day. One hundred students register to take one of three mathematics
courses: 51 students sign up for tenth-grade geometry, 30 for eleventh-grade algebra, and 19 for
twelfth-grade calculus. The school advertises small class sizes, and all classes have previously
been less than 22 students. Use Webster’s and Adam’s method to determine a quota and
apportionment (number of sections) for each math class based on a class size of 22 students.
Write a short conclusion discussing your findings.
Part 4: Sealed bids of estate
Lisa, Jerome, and Michael are heirs to their parents' estate in New York. The lawyer has
informed them that the estate consists of a house, a collectors' motorcycle, a Rolls Royce, a
Denver Broncos' season ticket. They are told to submit the bids by mail within 7 days. The
lawyer has listed their submitted bids as shown below. Describe the method of sealed bids and
then use the method of sealed bids to divide the estate among the heirs. Write a short conclusion
discussing your findings.
House Motorcycle Rolls Royce Ticket
Lisa
$40,000 $5,000
$35,000
$150
Jerome $38,000 $5,500
$27,000
$225
Michael $42,000 $4,300
$26,500
$300
Part 5: Going Separate Ways
After living together for a year, Emily, Kayla, and Kendra have decided to go their separate
ways. They have several items they bought together to divide, as well as some moving-out
chores. The values each place are shown below. Find the final allocation using method of
sealed bids. Write a short conclusion discussing your findings.
Emily Kayla Kendra
Dishes
20
30
40
Vacuum cleaner
100
120
80
Dining table
100
80
130
Detail cleaning
-70
-40
-50
Cleaning carpets
-30
-60
-50
Part 6: Lone Divider
1. Jon, Mark, Sally, and Susan are dividing a piece of land using the lone-divider method.
The values of the four pieces of land in the eyes of the each player are shown below.
Piece 1 Piece 2 Piece 3 Piece 4
a.
b.
c.
d.
e.
Jon
21%
27%
32%
20%
Mark
27%
29%
22%
22%
Sally
23%
14%
41%
22%
Susan
25%
25%
25%
25%
Who was the divider?
If playing honestly, what will each player’s declaration be?
Find the final division.
Write a short conclusion discussing your findings.
Describe the lone divider method.
Part 7: You split I choose
Dustin and Kendra want to split a bag of fun-sized candy, and decide to use the divider-chooser
method. The bag contains 100 Snickers, 100 Milky Ways, and 100 Reese's, which Dustin values
at $1, $5, and $2 respectively. (This means Dustin values the 100 Snickers together at $1, or
$0.01 for 1 Snickers). If Kendra is the divider, and in one half puts: 25 Snickers, 20 Milky
Ways, and 60 Reese's
a. What is the value of this half in Dustin's eyes?
b. Does Dustin consider this a fair share?
c. If Dustin was a divider, find a possible division that is consistent with his value
system.
d. Write a short conclusion discussing your findings.
Part 8: Fair
You will write a 1-2 page paper on what you have learned from apportionment and fair division.
Does fair always mean equal? What is fair? How are the seats in the House of Representatives
apportioned? Which method(s) favored larger states? Be sure to be specific and use what we
have done in class to support your answer.
Part 9: Honors only! Be a real representative
The U.S. House of Representatives has decided to decrease its membership by one. You will
need to reapportion the following states: Maryland, Virginia, West Virginia, Tennessee, North
Carolina, South Carolina, Mississippi, Alabama, Georgia and Florida. One of these states will
receive the extra representative. Visit 2010 US Census Apportionment Data and find the
population and number of representatives for each of the states that are in your region. Round the
population to the nearest tenth of a million (100,000). For example, a population of 16,725,415
would be rounded to 16.7 million. Use the Huntington-Hill number to make your determination.
Round the Huntington-Hill number to 4 decimal places. Make sure to show all work including
state names, populations, number of representatives, and Huntington-Hill numbers. Write a
conclusion statement discussing your findings.
Extra Credit
Write a one to two paper comparing and contrasting your definition of fair now given what you
have learned. Look at your paper you did at the beginning of the unit. How has your views
changed? Have they?
Other important stuff
1) You may either submit a hard copy or email me your report at brian.buri@robeson.k12.nc.us
2) Report should be in Times New Roman, 12 point font, double spaced, one inch
margins…Make it look nice and presentable.
3) You may do the work on a separate sheet of paper and turn it in with your rubric. You do not
need to type all of the work.
4) Project is due on Monday, March 24th, 2014. You must turn in your rubric in order for me to
grade your project.
5) Make sure that your report is "nice-looking" and that you double check the rubric to make sure
you have addressed all required information.
6) You will lose 15 points off for every day that your project is late for a maximum of 5 days.