Expanded House of Representatives

[jimrtex]

Montana, with nearly 1 million people should have at least 2 representatives in the House.

Based on the 2008 Estimates, Montana gets the 446th seat.

I also think that any state whose delegation constitutes more than 10% of the total House membership should be strongly encouraged to split into multiple states.

There is also something to be said about discouraging small states.  If instead of an automatic representative, we used Hamilton-Hill with a divisor of 1 to see if a state is eligible for a first representative, North Dakota, Wyoming, and Vermont would not get even their first Representative using the 2008 estimates. (A more generous divisor of 1/√2 would see all those states keep their Representatives, a less generous divisor of √2 would mean a state wouldn't get representatives until it had a large enough population to support 2 representative, except in the extraordinary case where the formula would give it the 435th and 436th Representatives.)

Incidentally, based on the 2008 estimates, if Puerto Rico became state and the House remains at 435 members, Ohio, Missouri, Minnesota, Illinois, California, and Texas would be the states that lose out on a representative each.

I thought it was Huntington-Hill.

If you take a state's population divide by average district population, square it and 1/4, then you have a representation entitlement for the State.  eg.  if Montana had a population equal to √2 of the average, then it would be entitled to 1.5 representatives.  If you are narrow-minded and insist on whole representatives, you would round this to 2.  But you could more equitably apportion 1.5 votes in the House, and have Montana elect two representatives who each exercise 0.75 votes.

Given that a State would receive v votes, if its relative population was p´=  (population/average) according to the formula.

v = √(p´² + 1/4)

Then a State would be entitled to exactly one vote if

p´ = √3/2.   In 2000, this would be around 560,000; such that VT, AK, ND, SD, DE, and MT were underrepresented.  WY would have been entitled to about 0.91 votes.

[jimrtex]

Wrote in a different H, my bad.
BTW, fixing the desired average at P/435, determining, then calculate v as you did and round each state to nearest, you end up with only 432 representatives.  Still, it does give a good first approximation to the result of Huntington-Hill.

That (432 representatives) is a feature.   Imagine for a moment that North Carolina qualified for its 13th representative on its own merit, that is:

(pnc/12)/(pusa/435) > (pusa/435)/(pnc/13)

or

pnc > √(13*12) * (pusa/435)

rather than on the relative lack of merit of Utah and other States.  Then, why if a 1000 people moved from North Carolina to South Carolina, why should Utah gain representation?  Just because North Carolina is further from 13/435 of the population, does not make Utah closer to 4/435 of the population.

Note that for ordinary distributions of State populations, more than the nominal number of representatives would be apportioned.  Currently, there are a rather large number of States with a population equivalent to less than (n + 1/2) representatives, than that are half way to the next representative.  Unless there is some effect where State populations are quantized such that populations tend to be separated by multiples of 1/435 of the US population, there will tend to be more balance than at present.

BTW, my own preferred system for determining the quota ∛P², has its own oddities.  In theory, with the 2008 pop. est. that would give 672 Representatives (∛P rounded to nearest integer), but it ends up giving only 670.

Also if Puerto Rico became a state, that would affect the population only enough to bring the target up 675, while Florida, Illinois, Minnesota, Mississippi, North Dakota, Pennsylvania, Texas, and Washington would each lose a Representative while Puerto Rico gained 9, bringing the House to only 671.