Apportionment
- 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