The Hamilton Method of Apportionment By G.S. .

The Hamilton Method of Apportionment

By G.S.

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When using the Hamilton Method, one first finds the Standard Divisor,

And then finds the quota, the fractional number of

representatives, for each state.

Standard Divisor = (Total Population) / (number of representatives)

s = pt/r

Quota = (State population) / (Standard Divisor)

q = ps/s

This process can be simplified by a little algebra.

s = pt/rq = ps/s 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.

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

The Hamilton Method solves this problem by temporarily assigning

each state its lower quota, the quota minus the fractional part,

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And then assigning the remaining representatives to the states with the largest difference between the

lower quota and the real quota.

Wisconsin (7.7 representatives) Maine (1.4 representatives)

9 person House:

(Numbers are fictional)All Images From: http://www.gpo.gov/fdsys/browse/collection.action?collectionCode=GPO&browsePath=Congressional+Pictorial+Directory

This seems to be fair, right? The fractions are dealt with by giving

the most deserving states the extra representatives.

Then why was this method nixed by the first presidential veto

in our nation’s history on ground

that it was unconstitutional?

The story starts in the first years of the United States, when several

apportionment schemes were investigated.

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?

?

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.

Veto!Don’t!

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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.

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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.

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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.


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Washington sided with Jefferson and Randolf and vetoed the bill, the first use of the presidential

veto ever.

Congress was unable to

override the veto, and

passed a bill legislating the

Jefferson Method.

This method was used until 1820.


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!



That’s a great story, but how does it apply to modern

apportionment and government?

First, by Jefferson and Randolf’s argument, our current method of

apportionment (Huntington-Hill) is unconstitutional.

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

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.

Bibliography• United States. Census Bureau. Apportionment Legislation 1790-1830. 2012. Web.

https://www.census.gov/history/www/reference/apportionment/apportionment_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.

The Hamilton Method of Apportionment By G.S. .

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