Apportionment Project This project is due on Wednesday, October 14, 2015



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Apportionment Project

This project is due on Wednesday, October 14, 2015 before midnight.  You must do your own work and may not share any parts of this project with others.  There will be a late penalty of 10 points per day for each school day the project is late. If you are absent the project will still be due on Wednesday. When you are finished with your project email it me at btapp@lincoln.k12.nc.us.



  • Your project should be submitted as a PDF file and titled YOUR_NAME_Apportionment_Project.pdf

  • Your project should not include any of the preliminary instructions. Please be sure it is organized with tables, worked out problems, and is professional looking.

  • When you have completed your project, make sure to double check your project with the rubric. Make sure that all required information is present.

Apportionment Project

Name:


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. Make sure to show all work and write a conclusion statement discussing the final apportionment. Round to three decimal places for all calculations. 


Part 2: Apportioning the Major League Baseball Competition Committee

Major League Baseball is adding one representative to its competition committee. Currently, the American League has 600 members and 8 representatives and the National League has 500 members and 7 representatives. Decide who should get the additional representative using any method you see fit. Make sure to show all work, justify your answer, and write a conclusion statement discussing your findings.

Part 3: The Other Methods and Paradoxes

States

A

B

C

Population

696

268

136



  1. State the standard divisor, standard quota, upper quota, and lower quota for each state.

  2. Distribute 10 seats using Webster’s Method with a modified divisor of 107.2.

  3. Distribute 10 seats using Jefferson’s Method with a modified divisor of 98.

  4. Determine the modified divisor needed so that Adam’s Method can be used to apportion the seats correctly. This will take trial and error until you get an apportionment that works when rounding all modified quotas up. (Hint: the modified divisor should be larger than the standard divisor when using Adam’s Method.) Once your modified divisor is determined, show the correct apportionment using Adam’s method.

  5. Distribute 10 sets using the Huntington-Hill Method. You will need to find a modified divisor if the standard divisor does not work.

  6. Discuss the quota rule, new-states paradox, population paradox, and the Alabama paradox in your own words. You may refer to your notes or cite an online resource.

Part 4: Method of Sealed Bids

Anne, Beth, and Jay are heirs to an estate that includes a computer, a used car, and a stereo. Each heir has submitted bids for the items in the estate as summarized in the following table. Find the final settlement for each heir after applying the method of sealed bid in the table below.







Anne

Beth

Jay

Computer

$1,800

$1,500

$1,650

Car

$2,600

$2,400

$2,000

Stereo

$1,000

$800

$1,200







Anne

Beth

Jay

Total of bids










Fair share










Items received










Value of items received










Initial Cash paid or received










Share of remaining cash










Final settlement












  1. Summarize in sentence form what each person receives or pays in terms of money or items.

  2. Should each person be satisfied using the method of sealed bids? Explain why or why not.

Part 5: Determine the Best Way

Three children (Abby, Bryan, and Chloe) are dividing the array of nine candy pieces shown in the following figure. The players’ markers are indicated in the figure (with A for Abby, B for Bryan, and C for Chloe). Abby for example, divides the candy into three intervals of what she would consider fair (Candy Piece 1/Candy Piece 2 through Candy Piece through Candy Piece 5/Candy Piece 6 through Candy Piece 9). Determine the best way to evenly allocate the candy so that everyone is satisfied based on their preferences. Clearly explain your method.



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