The Hamilton Method of Apportionment

1. The Hamilton Method of Apportionment By G.S. http://pabook.libraries.psu.edu/palitmap/ArticlesHamilton.jpg

2. When using the Hamilton Method, one first finds the Standard Divisor, Standard Divisor = (Total Population) / (number of representatives) s = pt/r And then finds the quota, the fractional number of representatives, for each state. Quota = (State population) / (Standard Divisor) q = ps/s

3. This process can be simplified by a little algebra. q = ps/s s = pt/r and So by substitution, q = ps/(pt/r) Multiply both numerator and denominator by r, q = (ps/pt)*r Or, in English, The quota equals the population of the state divided by the total population and then multiplied by the total number of representatives.

4. The problem occurs when the quota contains a fraction, as a state can’t have a fraction of a representative. All Images From: http://www.gpo.gov/fdsys/browse/collection.action?collectionCode=GPO&browsePath=Congressional+Pictorial+Directory

5. The Hamilton Method solves this problem by temporarily assigning each state its lower quota, the quota minus the fractional part, All Images From: http://www.gpo.gov/fdsys/browse/collection.action?collectionCode=GPO&browsePath=Congressional+Pictorial+Directory

6. And then assigning the remaining representatives to the states with the largest difference between the lower quota and the real quota. 9 person House: Maine (1.4 representatives) Wisconsin (7.7 representatives) (Numbers are fictional) All Images From: http://www.gpo.gov/fdsys/browse/collection.action?collectionCode=GPO&browsePath=Congressional+Pictorial+Directory

7. This seems to be fair, right? The fractions are dealt with by giving the most deserving states the extra representatives.

8. Then why was this method nixed by the first presidential veto in our nation’s history on ground that it was unconstitutional?

9. The story starts in the first years of the United States, when several apportionment schemes were investigated.

10. The first bill, “An Act for an apportionment of Representatives among the several States according to the first enumeration,” legislated the Hamilton Method, and narrowly passed both houses of Congress, which had chosen it over the Jefferson Method of apportionment. ? But was it constitutional?

11. Washington’s advisors were split on this issue, with his Attorney General Edmund Randolf and Secretary of State Thomas Jefferson supporting a veto, and Secretaries of War and the Treasury Henry Knox and Alexander Hamilton opposing one. http://s.fixquotes.com/files/author/thomas-jefferson_hYcfr.jpg http://pabook.libraries.psu.edu/palitmap/ArticlesHamilton.jpg Veto! Don’t! http://teachingamericanhistory.org/ratification/images/randolph.jpg http://www.artsunlight.com/NN/N-S0007/N-S0007-095-henry-knox.jpg

12. Randolf and Jefferson believed the act was unconstitutional because it did not apply the same divisor to each state, therefore treating voters unequally. The constitution dictated “an apportionment,” and this was really two: one for the lucky states and one for everyone else. One man, one vote. http://s.fixquotes.com/files/author/thomas-jefferson_hYcfr.jpg http://teachingamericanhistory.org/ratification/images/randolph.jpg

13. They also believed that a common divisor should be found, and each state’s population divided by that number to establish the total number of representatives, instead of using the total number of representatives to find the divisor for each state. This could lead to a strange number of representatives, like 231 or 437. http://stc.obolog.net/photos/4f77/4f776ee84aeees17120_b.jpg

14. Knox and Hamilton, on the other hand, believed the constitution was vague enough on this issue that it could go either way. As Washington didn’t have a huge political interest either way and this method caused no serious problems, he should allow the democratically elected Congress to do as they wished as a more direct manifestation of the people. Congress is pretty cool, too. http://pabook.libraries.psu.edu/palitmap/ArticlesHamilton.jpg http://www.artsunlight.com/NN/N-S0007/N-S0007-095-henry-knox.jpg

15. Washington sided with Jefferson and Randolf and vetoed the bill, the first use of the presidential veto ever.

16. Congress was unable to override the veto, and passed a bill legislating the Jefferson Method. http://s.fixquotes.com/files/author/thomas-jefferson_hYcfr.jpg This method was used until 1820.

17. The Jefferson Method has problems, too (it unfairly favors large states), but it finds a modified standard divisor that divides each population evenly, making it constitutional by Jefferson’s logic. Constitutional! Unfair! http://s.fixquotes.com/files/author/thomas-jefferson_hYcfr.jpg http://pabook.libraries.psu.edu/palitmap/ArticlesHamilton.jpg

18. That’s a great story, but how does it apply to modern apportionment and government?

19. First, by Jefferson and Randolf’s argument, our current method of apportionment (Huntington-Hill) is unconstitutional.

20. Second, the guys who literally wrote the constitution had serious issues interpreting it. It’s no surprise that we have trouble as well. Cut us a break! http://upload.wikimedia.org/wikipedia/commons/d/db/Supreme_Court_US_2009.jpg

21. In conclusion, the Hamilton Method and the first apportionment schemes of our country have a fascinating history that contains valuable lessons for the future of our democracy.

22. Bibliography • United States. Census Bureau. Apportionment Legislation 1790-1830. 2012. Web. https://www.census.gov/history/www/reference/apportionment/apportio nment_legislation_1790 • "A Brief History of Apportionment." Thirty-Thousand. N.p., n.d. Web. 15 Apr 2013. <http://www.thirty-thousand.org/pages/Apportionment.htm>. • "Apportionment." Ohio State University. Ohio State University, 06 February 2013. Web. 15 Apr 2013. • Balinski, M.L., and H.P. Young. "The Quota Method of Apportionment." American Mathematical Monthly. 82.7 (1975): 701-730. Web. 15 Apr. 2013.