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CHAPTER 14:
APPORTIONMENT
I.
Basics
Example 1:
Suppose a country consists of five states (North, South, East, West and Central) and representation in the
National Assembly should be in proportion to each state’s population.
The latest census figures are:
North
9279
South
7217
East
5155
West
3093
Central
2062
Total
26,806
If there are 26 seats in the Assembly, how should they be apportioned among the five states?
Solution:
Let’s start by dividing the total population by the number of seats: ___________ .
This tells us how many
citizens each member of the National Assembly represents and is called the
standard divisor
.
The number of seats each state is entitled to,
called its
quota
, is
North’s quota is _________ South’s quota is _________ East’s quota is _________
West’s quota is _________
Central’s quota is _________
The two formulas above can be combined to yield:
Example 2:
Suppose a later census is taken and the following population figures are revealed.
How should the 26 seats be apportioned among the 5 states?
Solution:
Notice the quotas aren’t whole numbers any more. Round them off, you say?
Std. Divisor = 1000
Standard Rounded
State
Population
Quota
Quota
North
9061
South
7179
East
5259
West
3319
Central
1182
Total
26000
Standard Divisor:
That doesn’t work either since the rounded quotas sum to 25, not 26.
One state has to gain a seat here.
The question is
which one?
First, some vocabulary.
If we round down, we get what is called the
lower quota
.
If we round up, we get what is
called the
upper quot
a
.
The following notation is used:
9
061
.
9
=
and
10
061
.
9
=
Chapter 14
Page 1
State’s quota =
seats
of
number
population
total
population
s
State
⋅
'
Standard Divisor =
seats
of
number
total
population
total
State’s quota =
'
tan
state s population
s
ard divisor
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View Full Document This problem of the rounded quotas not summing to the desired number is quite common.
Sometimes the rounded
quotas sum to a number that is too big.
This problem became apparent in the late 18
th
century.
The U.S. Constitution,
while requiring that the House of Representatives be apportioned proportional to each state’s population, didn’t spell out a
precise method for doing this.
Nor did it specify the size of the House.
The first census was taken in 1790, 3 years after the
Constitutional Convention.
We are going to study five methods for solving this problem.
One method considered by
Congress, and the easiest to use, was advocated by Alexander Hamilton, America’s first Secretary of the Treasury.
II.
Hamilton’s method
consists of three steps:
1. Calculate each state’s standard quota.
2. Give to each state a number of seats equal to its lower quota.
3. Give the remaining seats, one at a time, to the states with the largest decimal parts until
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This note was uploaded on 01/04/2012 for the course MGF 1107 taught by Professor Storfer during the Fall '08 term at FIU.
 Fall '08
 Storfer

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