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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 Spring '08
 EVINSON
 Math, Calculus, Ratio, Fraction, Natural number, United States Secretary of the Treasury

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