[EM] [Fwd: Re: Apportionment (biased?) let me add some more confusion to the mix :)]

[Dave Ketchum]

What is Hamilton's method?

Before exploring that, my proposal had two parts:
       EVERY state SHALL have at least the number of seats they earn with
fractions ignored.
       While I may have got to Hamilton with my words as to disposing of
fractions, I suggest that others may be able to do better with this part.

I question whether monotonicity, etc., can justify failing to honor the
part I demand.

While labels can be convenient, we too often have different definitions
behind the names.  For example, in "Method of Apportionment",
www.census.gov says that Hamilton was used 1850-1900, and includes a
paragraph describing it.  While they mention the problem of low population
states elsewhere, they do not mention such in their description of Hamilton.

While Israel could have trouble with small parties, we do not have enough
small states to need better than what we have - if they got to be a
problem, combining a few such states would be a possibility.
       New York disposes of too small parties by refusing to give any
support to those that are too weak.

DWK

On Sun, 10 Dec 2006 22:30:05 -0500 Joseph Malkevitch wrote:
 > Dear David,
 >
 > In essence what you are describing is Largest Remainder or Hamilton's
 > Method. If the house size is allowed to change this method does not obey
 > house monotonicity. It also violates various "population monotonicity"
 > axioms. The house size is currently fixed so that is not a problem. If
 > you do not mind that population monotonicity can be violated then you
 > can promote Largest Remainder. There is also some consideration whether
 > or not this method may or may not advantage "smaller" vs. "larger"
 > states. Israel used to us this system and had lots of troubles with many
 > small parties. Eventually it moved to D'Hondt. In the European version
 > of the apportionment problem there are typically requirements that
 > parties get a minimum percentage of the vote to get any seats.
 >
 > Regards,
 >
 > Joe
 >
 >
 >
 >
 >
 > On Dec 10, 2006, at 9:22 PM, Dave Ketchum wrote:
 >
 >> I suggest the following as a proposed LIMIT on the fancy finagling:
 >>
 >> Calculate persons per district as (total persons)/(legislature size).
 >>
 >> Since this is for Congress, every state earning less than one whole
 >> seat gets one, with no consideration as to fractions - period.
 >>
 >> Each other state gets the whole seats they have earned - period.
 >>
 >> I CLAIM that each state has earned the above and should get ALL of
 >> that - period.
 >>
 >> So there are some leftover fractions we can debate, but debate limited
 >> to these - trying to avoid Alabama and other paradoxes is restricted
 >> to allocation of these fractions.
 >>
 >> I propose, without arguing against whoever may claim to do better:
 >>      Sort the fractions as to size, with largest sizes each getting
 >> one of the leftover seats.  If the end of this requires deciding among
 >> identical fractions, assign among these randomly.
-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
            Do to no one what you would not want done to you.
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