Apportionment

ALI CABAN

BRYNNA DOWNEY

SARAH JACKSON

Apportionment of House representAtives for 50 stAtes,

D.C., AnD puerto riCo

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)

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)

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

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

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)

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 = 0Uh oh! Jefferson Method doesn’t

work too well

















Kansas 4 ND 0


Adams Method

Steps:


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.

Webster Method

Steps:


2. Compute mQ, the modified quota for each statemQ = 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.


(1840 – 1850)(1910 – 1940 )

Hill-Huntington Method

Steps:


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.


(1940 – present)

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

















Kansas 4 ND 1


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

















Kansas 4 ND 1

Kentucky 6 Ohio 16 Total: =435

Sports

Apportionment