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The Apportionment Problem

An exploration of the apportionment problem in mathematical and political contexts.

Benjamin Fisher
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Assignment 1: The Apportionment ProblemYou are a census officer in a newly democratic nation and you have been charged with using the censusdata from the table below to determine how 100 congressional seats should be divided among the 10states ofthe union.StatePopulation11547523564439875648834653696856637434278843119547301025467Being a fan of United States history, you are familiar with the many methods of apportionment applied tothisproblem to achieve fair representation in the US House of Representative. You decide thatapportionment (chapter 11, sections 1-4 in your textbook) is the best approach to solving this problem,but need to compare several methods and then determine which is actually fair.1.Using the Hamilton method of apportionment, determine the number of seats each state shouldreceive.2.Using the numbers you just calculated from applying the Hamilton method, determine theaverage constituency for each state. Explain your decision making process for allocating theremaining seats.3.Calculate the absolute and relative unfairness of this apportionment.4.Explain how changes in state boundaries or populations could affect the balance ofrepresentation in this congress. Provide an example using the results above.5.How and why could an Alabama Paradox occur?6.Explain how applying the Huntington-Hill apportionment method helps to avoid an AlabamaParadox.7.Based upon your experience in solving this problem, do you feel apportionment is the best way toachieve fair representation? Be sure to support your answer.8.Suggest another strategy that could be applied to achieve fair representation either usingapportionment methods or a method of your choosing.You may perform your own calculations or use theExcel spreadsheet hereto assist you. You must showsome calculations in your document to demonstrate that you know how to perform these tasks.This is the grading criteria!!Assignment 2 Grading CriteriaMaximumPointsAssignment Components

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