The document discusses the different methods that have been used throughout history to apportion seats in the US House of Representatives among the states based on population. It explains the Hamilton, Jefferson, Adams, and Webster methods used between 1790-1940, and the current Hill-Huntington method. Each method involves calculating quotas and modified divisors and rounding quotas up or down to determine the number of seats each state receives. The document provides examples applying each method to the populations of Alabama and DC.

1. ALI CABAN
BRYNNA DOWNEY
SARAH JACKSON
Apportionment of House
representAtives for 50 stAtes,
D.C., AnD puerto riCo

2. What is Apportionment?
Distributing something
proportionally to different
groups
Apportion house
representatives to the US
states based on state
population
We figure out population of
states and country from
census (residents, not
including green card
holders)

3. Hamilton Method
1. Compute the standard divisor,
d = total population/total number of
seats
2. Compute the standard quota for each
state, Q = state’s population/d
3. Round each state’s standard quota Q
down to the nearest integer. Each state will
get at least this many seats, but must get at
least one.
4. Give any additional seats one at a time
(until no seats are left) to the states with
the largest fractional parts of the their
standard quotas.
Used: (1850 – 1900)

4. Hamilton Method in Action (Alabama + D.C.)
Alabama
1. Standard divisor,
d= total pop/house seats
d=320,820,975/435
d= 737,519.48
2. Alabama Standard Quota,
Q=state pop/d
Q=4,802,982/737,519.48
Q= 6.51
3. Round Q down to nearest integer
(must be at least 1)
New Q = 6
D.C.
1. Total pop/house seats
d = 737,519.48
2. D.C. Standard Quota
Q = state pop/d
Q = 601,723 / 737,519.48
Q = 0.82
3. Round Q down to nearest integer
(must be at least 1)
New Q = 0 (must be at least 1
though!)
New Q = 1

5. Alabama 6 Louisiana 6 Oklahoma 5
Alaska 1 Maine 2 Oregon 5
Arizona 9 Maryland 8 Penn. 17
Arkansas 4 Mass. 9 PR 5
California 51 Michigan 13 RI 1
Colorado 7 Minnesota 7 SC 6
Conn. 5 Mississippi 4 SD 11
Delaware 1 Missouri 8 Tennessee 9
D.C. 1 Montana 1 Texas 34
Florida 26 Nebraska 2 Utah 4
Georgia 13 Nevada 4 Vermont 1
Hawaii 2 NH 2 Virginia 11
Idaho 2 NJ 12 Wash 9
Illinois 17 NM 3 WV 3
Indiana 9 NY 26 Wisconsin 8
Iowa 4 NC 13 Wyoming 1
Kansas 4 ND 1
Kentucky 6 Ohio 16 Total: 435

6. Jefferson Method
Steps:
1. Compute md, the modified divisor.
2. Compute mQ, the modified quota
for each state.
mQ = state’s population/md
3. Round each state’s modified quota mQ
down to the nearest integer.
4. Give each state this integer number of
seats.Used: (1790 – 1840)

7. Jefferson Method in Action (Alabama + D.C.)
Alabama
1. Modified divisor (a number I
made up)
md= 739,000
2. Modified Quota,
mQ=state pop/md
mQ=4,802,982/739,000
mQ= 6.499
3. Round mQ down to nearest
integer
New Q = 6
D.C.
1. Total pop/house seats
md= 739,000
2. D.C. Modified Quota
mQ = state pop/md
mQ = 601,723 / 739,000
mQ = 0.82
3. Round Q down to nearest
integer
New Q = 0
Uh oh! Jefferson Method doesn’t
work too well

8. Alabama 6 Louisiana 6 Oklahoma 5
Alaska 1 Maine 1 Oregon 5
Arizona 9 Maryland 8 Penn. 18
Arkansas 4 Mass. 9 PR 5
California 53 Michigan 14 RI 1
Colorado 7 Minnesota 7 SC 6
Conn. 5 Mississippi 4 SD 11
Delaware 1 Missouri 8 Tennessee 9
D.C. 0 Montana 1 Texas 36
Florida 27 Nebraska 2 Utah 3
Georgia 14 Nevada 3 Vermont 0
Hawaii 2 NH 1 Virginia 11
Idaho 2 NJ 12 Wash 9
Illinois 18 NM 2 WV 2
Indiana 9 NY 28 Wisconsin 8
Iowa 4 NC 13 Wyoming 0
Kansas 4 ND 0
Kentucky 6 Ohio 16 Total: 435

9. Adams Method
Steps:
1. Compute md, the modified
divisor.
2. Compute mQ, the modified quota
for each state.
3. Round each state’s modified quota
mQ up to the nearest integer.
4. Give each state this integer number
of seats.

10. Webster Method
Steps:
1. Compute md, the modified divisor.
2. Compute mQ, the modified quota for
each state
mQ = state’s population/md
3. Round each state’s modified quota mQ
up to the nearest integer if its fractional part
is greater than or equal to .5 and down to
the nearest integer if its fractional part is
less than .5.
4. Give each state this integer number of
seats.
(1840 – 1850)
(1910 – 1940 )

11. Hill-Huntington Method
Steps:
1. Compute md, the modified divisor.
2. Compute mQ, the modified quota for each
state.
3. Take two integers, one is mQ rounded up, the
other is mQ rounded down. Take geometric mean
(square root of mQ1*mQ2). If mQ is less than
geometric mean, round down. If mQ is greater than
it, round up.
4. Give each state this integer number of seats.
(1940 – present)

12. Hill-Huntington Method in Action (Alabama and
D.C.)
Alabama
1. Modified divisor (a number I made up)
md= 745,000
2. Modified Quota,
mQ=state pop/md
mQ=4,802,982/745,000
mQ= 6.446
3. Round mQ down and up to nearest
integer
New Q = 6/7
4. Geometric mean = sqrt(6*7) = 6.48
mQ < Geometric mean, so we round
down
5. Reps = 6
D.C.
1. Total pop/house seats
md= 745,000
2. Modified Quota
mQ = state pop/md
mQ = 601,723 / 745,000
mQ = 0.808
3. Round Q down and up to nearest
integer
New Q = 0/1
4. Geometric mean = sqrt(0*1) = 0
mQ > Geometric mean, so we round up
5. Reps = 1

13. Alabama 6 Louisiana 6 Oklahoma 5
Alaska 1 Maine 2 Oregon 5
Arizona 9 Maryland 8 Penn. 17
Arkansas 4 Mass. 9 PR 5
California 50 Michigan 13 RI 2
Colorado 7 Minnesota 7 SC 6
Conn. 5 Mississippi 4 SD 11
Delaware 1 Missouri 8 Tennessee 9
D.C. 1 Montana 1 Texas 34
Florida 25 Nebraska 3 Utah 4
Georgia 13 Nevada 4 Vermont 1
Hawaii 2 NH 2 Virginia 11
Idaho 2 NJ 12 Wash 9
Illinois 17 NM 3 WV 3
Indiana 9 NY 26 Wisconsin 8
Iowa 4 NC 13 Wyoming 1
Kansas 4 ND 1
Kentucky 6 Ohio 16 Total: 435

14. Works Cited
Pictures
 http://www.post448.org/images/AlexanderHamilton.jpg
 http://www.biography.com/imported/images/Biography/Ima
ges/Profiles/J/Thomas-Jefferson-9353715-1-402.jpg
 http://www.biography.com/imported/images/Biography/Ima
ges/Profiles/A/John-Quincy-Adams-9175983-1-402.jpg
 http://upload.wikimedia.org/wikipedia/commons/thumb/2/2
b/Daniel_Webster_-_circa_1847.jpg/220px-
Daniel_Webster_-_circa_1847.jpg
 http://www.census.gov/history/img/jahill.jpg
 http://www.profcardy.com/matematicos/bHuntington.jpg

15. Alabama 7 Louisiana 6 Oklahoma 5
Alaska 1 Maine 2 Oregon 5
Arizona 9 Maryland 8 Penn. 18
Arkansas 4 Mass. 9 PR 0
California 53 Michigan 14 RI 2
Colorado 7 Minnesota 8 SC 7
Conn. 5 Mississippi 4 SD 1
Delaware 1 Missouri 8 Tennessee 9
D.C. 0 Montana 1 Texas 36
Florida 27 Nebraska 3 Utah 4
Georgia 14 Nevada 4 Vermont 1
Hawaii 2 NH 2 Virginia 11
Idaho 2 NJ 12 Wash 10
Illinois 18 NM 3 WV 3
Indiana 9 NY 27 Wisconsin 8
Iowa 4 NC 13 Wyoming 1
Kansas 4 ND 1
Kentucky 6 Ohio 16 Total: =435