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The Problem Of Apportionment

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THE APPORTIONMENT PROBLEM Abstract: There are two critical elements in the dictionary definition of the word ‘Apportion’ : 1. We are dividing & assigning things, and 2. We are doing this on a proportional basis & in a planned, organized fashion. Apportionment is the problem of translating an election outcome to a number of seats in fixed-size political house. Mathematically, the problem consists of translating a sequence of reals to a sequence of integers, while ensuring that the sum of the sequence sums to a pre-determined number. The problem arises because seats are indivisible, whereas an election outcome generally gives rise to fractional remainders. Introduction: How should I divide a bag of peanuts among my six cousins? How should Uncle Sam divide his property among his 5 “sons”? How should the House of Representatives assign its 435 seats to the 50 states which make up the union? …show more content…

The apportionment problem is a problem which has no ‘one’ correct answer. Instead of being given an answer to a problem, the reader will learn how to ask questions which can be answered, and make use of the answers. This process includes deciding upon objectives, building algorithms to obtain those objectives, determining whether the algorithms will work within reasonable time constraints, and determining when two algorithms achieve the same final output. Apportionment is an especially timely topic following the decennial census (1990, 2000, etc.) when the U. S. House of Representatives is

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