Apportionment Methods

1
Apportionment Methods
2
Apportionment

• Apportionment means distribution or allotment in
  proper shares.
• (related to Fair Division)

3

• In the context of the Constitution, apportionment
  means that each state gets a number appropriate
  to its population. For example, Representatives
  are apportioned among the states, with the most
  populous getting the greater share.

4

• Two terms that need to be understood
• Standard Divisor (what you divide by)
• Standard Quota (the result of your division)

5
Standard Divisor

• The Standard Divisor determines the number of
  people needed to get one seat in Congress
• Standard Divisor Total Population
• of seats

6
Standard Quota

• The Standard Quota determines the number of seats
  a particular group deserves
• Standard Quota population of subgroup
• standard divisor

7
Example

• 1440 students at CHS and 30 seats in the student
  senate
• 1440/30 48 needed to get a seat (Standard
  Divisor)
• Senior class has 328 students
• 328/48 6.83 seats for Seniors in the student
  senate (Standard Quota)
• 6.83 Seats 6.83 Seniors???

8
The Apportionment Problem

• How do we turn the fractions into whole people?

9
Lower Upper Quotas

• The standard quota numbers need to be rounded to
  a whole number.
• The Lower Quota is the standard quota rounded
  down to the nearest whole number
• The Upper Quota is the standard quota rounded up
  to the nearest whole number

10

• There have been four different apportionment
  methods over the history of this country.
• Today we will learn about the simplest method

11
Hamiltons Method

• This was Alexander Hamiltons attempt to deal
  with the Apportionment Problem
• There are 3 steps to Hamiltons Method
• 1) Calculate each groups standard quota
• 2) Round each standard quota down (lower quota),
  and give each group that number
• 3) Give the surplus items one at a time to the
  groups with the largest decimal parts

12
For Example

• CHS 1440 students with 30 seats in student
  senate
• Number of students in each grade
• Seniors 328
• Juniors 346
• Sophomores 351
• Freshmen 415

13
Hamiltons Method

• There are 3 steps to Hamiltons Method
• Calculate each groups standard quota
• Standard divisor 1440/30 48 students per
  seat
• Standard quotas
• Seniors 328/48 6.83
• Juniors 346/48 7.21
• Sophomores 351/48 7.31
• Freshmen 415/48 8.65

14
Hamiltons Method

• There are 3 steps to Hamiltons Method
• 2) Round each standard quota down (lower quota),
  and give each group that number of seats
• Standard quotas (adjusted)
• Seniors 328/48 6.83 becomes 6
• Juniors 346/48 7.21 becomes 7
• Sophomores 351/48 7.31 becomes 7
• Freshmen 415/48 8.65 becomes 8

15
Hamiltons Method

• There are 3 steps to Hamiltons Method
• 3) Give the surplus items one at a time to the
  groups with the largest decimal parts
• Standard quotas (adjusted)
• Seniors 328/48 6.83 becomes 6 Only 28 seats
  have
• Juniors 346/48 7.21 becomes 7 been used
• Sophomores 351/48 7.31 becomes 7
• Freshmen 415/48 8.65 becomes 8

16
Hamiltons Method

• There are 3 steps to Hamiltons Method
• 3) Give the surplus items one at a time to the
  groups with the largest decimal parts
• Standard quotas (adjusted)
• Seniors 328/48 6.83 becomes 7 (gets an
  additional seat)
• Juniors 346/48 7.21 becomes 7
• Sophomores 351/48 7.31 becomes 7
• Freshmen 415/48 8.65 becomes 9 (gets an
  additional seat)

17
Hamiltons Method

• There are 3 steps to Hamiltons Method
• 3) Give the surplus items one at a time to the
  groups with the largest decimal parts
• Standard quotas (adjusted) Final Apportionment
• Seniors 328/48 6.83 became 7 Seniors have 7
  seats
• Juniors 346/48 7.21 remained 7 Juniors have 7
  seats
• Sophomores 351/48 7.31 remained 7 Sophomores
  have 7 seats
• Freshmen 415/48 8.65 became 9 Freshmen have 9
  seats

18
Homework, Homework, Homework I know you love
your homework

• P. 760-761 1-5