mgf1107lecture9 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 9 Chapter 4 – The Mathematics of Apportionment In chapter 3 we looked at how to divide a given object, such as a cake or an inheritance based on the notion of a fair share. In a sense it was all based on the notion of equality, since everyone received an amount with which they were satisfied. In this chapter we will consider uneven distributions, generally of people, based on regional population differences. Definitions and Notation The N states represent the parties that have a stake in the apportionment. The seats are the M (identical) objects to be divided. The populations are the number of people in each state. The standard divisor is the ratio of the total population to the number of seats. The standard quota is the ratio of each state’s population to the standard divisor and is denoted by q. If q is a fraction, then the upper quota is the value of q rounded up to the next whole number, and the lower quota is the value of q rounded down to the next whole number.
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mgf1107lecture9 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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