[EM] The History of Apportionment

Narins, Josh josh.narins at lehman.com
Wed Mar 13 07:42:45 PST 2002

Apportionment, another math in Politics.

Apportionment is the process, done every 10 years after the census, of
giving a share of the total 435 Representatives to each of the 50 States.
Constitutionally, the only requirements are that each State must have at
least one Rep, and there can't be more than one Rep per 30,000 people.
Alexander Hamilton invented the first equation used to apportion US
Representatives (at least, he gets credit for it). As you can see here,
http://w3.fiu.edu/math/html/gazzette/fall96.htm, it's bad.
We've used other methods, they were all flawed.
In 1920s things started getting pretty darn contentious over apportionment.
There were tiny districts and huge districts, and it was quite imbalanced.
Later, the Supreme Court actually ruled that the standard deviation of the
populations of the districts in one State must be minimal (1).
In 1929, Congress gave orders to the National Academy of Sciences(NAS) to
investigate the best way to apportion Representatives, mathematically
Well, NAS, not to be hasty, took over a decade to complete their research.
In 1941, the NAS got back to Congress with five possible solutions. Congress
didn't take long in deciding that the "Method of the Harmonic Mean" was
fairest (2), and we've been using that method ever since.

Like apportionment, Voting systems are mathematically complex notions, where
a seemingly reasonable solution. making the winner the person who gets the
most votes) is actually a bad thing.

Here is where I should have a list of all Presidents who would not have won
with a more sophisticated system.
Lincoln would have lost == No or delayed Civil War
Clinton would have lost (the 1st time)
Bush the Second would have lost

Doesn't really matter where you are on the political spectrum, I imagine,
someone you don't like got elected with primitive voting systems.

(*) Can you imagine today's Supreme Court recognizing anything to do with
(2) I agree. It's a nice thing. There is one flaw, though, unrelated to the
method, but the cap. The 2000 apportionment would have been fairer (by
measurement of the standard deviation of all districts) with only 432 Reps
instead of 435. Oh well. Sorry, I might have been able to do something about

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