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

[Dave Ketchum]

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.

DWK

On Sun, 10 Dec 2006 18:05:50 -0500 Joseph Malkevitch wrote:
> Dear Election List,
> 
> If you look at the technical papers on apportionment, especially 
> Balinski and Young's work, you will see that one of the most difficult 
> problems to address is the issue of "ties." Ties not only occur when two 
> states have identical population but also when you apply the divisor 
> interpretation of the the "divisor" methods. Loosely speaking the reason 
> why divisor methods violate not giving a state the integer above or 
> below its exact quota (when its exact number of seats that should be 
> given to it is not an integer) is that states of about the same 
> population (not to mention exactly equal population) should be treated 
> equally from the pairwise equity point of view. What this means is that 
> Webster, say, will give the same number of seats to states with 
> approximately the same population even if this means being overly 
> generous or ungenerous to other states. Thus, loosely speaking, these 
> methods try to treat equally situated states in an equivalent manner 
> even if this means that "quota" (as defined above) gets violated. One 
> way to try to get around this is to use discrete optimization methods 
> that optimize some global criterion rather than look at pairwise equity. 
> 
> Note that Balinski and Young have a "technical meaning" for the word 
> "bias." 
> 
> Regards,
> 
> Joe
> Joseph Malkevitch
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  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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