[EM] Would would you say about a method that gives a seat to a 1-person state?

[Dan Bishop]

raphfrk at netscape.net wrote:
>  > From: nkklrp at hotmail.com
>  >
>  > The examples dramatize Hill's bias, but would could be more dramatic than
>  > this?:
>  >
>  > If we dildn't have the 1-free-seat-for-each-state rule, Hill would give
>  > everyone a seat anyway, but Hill's own rules. It would give a seat to any
>  > state that contains at least one person. How do you like that for 
> dramatic
>  > bias.
> 
> That is pretty cool, it will comply with the 1 seat per State rule 
> 'natively'.
> 
> Pity about the additional bias for higher numbers of seats.
> 
>  > If you had any doubt about Hill's bias, that should settle the matter.
>  > Someone might say, "But that doesn't happen, due to the free seats".
> 
> Right.  Also, how small is the smallest State ?

Wyoming has about half a million people.

>  > While Hill's round-up point between 0 and 1 is at 0, Bias-Free's round-up
>  > point in that range is near .38  That is, 1/e. Webster's round off 
> point in
>  > that range, of course, is at .5  So, though Webster is biased, it's bias
>  > isn't of the dramatic nature of Hill's bias.
> 
> Recognising that all States get 1 seat anyway, the critical point is for
> numbers greater than 1.  I guess Webster is 1.5 and Hill is lower than
> that ?

Correct.  Hill's cutoff is sqrt(2) = 1.4142135623730951.  Not that far 
from the Webster cutoff; in fact, as I've mentioned before, Webster and 
Hill give identical apportionments this decade.

>  > Unbias is absolutely essential for House apportionment. That means that
>  > Hamilton and Bias-Free are the only methods that can be considered for
>  > apportionment.
> 
> It seems to me that they are all reasonably close.  Unless you get rid of
> the 2 Senators per State rule, slight biases in the House apportionment
> are not very significant.

Furthermore, you could get a much better improvement in proportionality 
by increasing the size of the House than by changing the apportionment 
method.

> If you are going to settle for Webster, then settling for Hill isn't a major
> additional compromise.

Agreed.