Transcript Apportionment (5/4)

Apportionment
 Apportionment means distribution or
allotment in proper shares.
(related to “Fair Division”)
 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.
 Two terms that need to be understood:
 Standard Divisor (what you divide by)
 Standard Quota (the result of your division)
Standard Divisor
 The Standard Divisor determines the number of
people needed to get one seat in Congress
 Standard Divisor = Total Population
# of seats
Standard Quota
 The Standard Quota determines the number of
seats a particular group deserves
 Standard Quota = population of subgroup
standard divisor
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???
The Apportionment Problem
 How do we turn the fractions into whole
people?
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
 There have been four different apportionment
methods over the history of this country.
 Today we will learn about the simplest method…
Hamilton’s Method
 This was Alexander Hamilton’s attempt to
deal with the Apportionment Problem
 There are 3 steps to Hamilton’s Method:
1) Calculate each group’s 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
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
Hamilton’s Method
 There are 3 steps to Hamilton’s Method:
1)
Calculate each group’s 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
Hamilton’s Method
 There are 3 steps to Hamilton’s 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
Hamilton’s Method
 There are 3 steps to Hamilton’s 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
 Juniors = 346/48 =7.21 becomes 7
 Sophomores = 351/48 = 7.31 becomes 7
 Freshmen = 415/48 = 8.65 becomes 8
Only 28 seats have
been used…
Hamilton’s Method
 There are 3 steps to Hamilton’s 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)
Hamilton’s Method
 There are 3 steps to Hamilton’s 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 became 7
Final Apportionment:
Seniors have 7 seats
 Juniors = 346/48 =7.21 remained 7
Juniors have 7 seats
 Sophomores = 351/48 = 7.31 remained 7Sophomores have 7 seats
 Freshmen = 415/48 = 8.65 became 9
Freshmen have 9 seats
Homework, Homework, Homework;
I know you love your homework…
 P. 760-761; #1-5