[EM] Joe: Bias

[Joseph Malkevitch]

Dear Elections List,


On Dec 9, 2006, at 3:13 PM, MIKE OSSIPOFF wrote:

>
> Joe--
>
> You wrote:
>
>
> The issue of whether or not a particular method of apportionment is
> biased is rather complex it seems to me.
>
> I reply:
>
> If we consistently and systematically give more seats per person to  
> smaller states,


What is your definition of a small state?



> that is biased.
> That's what Hill does. Hill is biased.


How do YOU measure bias?

Can you provide the data for bias based on your definition of small  
state and bias?

Furthermore, apportionments can be used for other problems other than  
the US House of Representatives. Does this data show no bias too?




>
> That's what bias is: A systematic disparity in seats per person.  
> Plainly Hill has that, and plainly Webster does not have it.  
> Complex? I suggest that Huntington and Hill invented complexity  
> that isn't really there.
>
> I agree that Huntington and Hill managed to obfuscate the subject  
> for Congress, and may have come up with their own creative and  
> complicated definitions of prioportionality and bias. But those  
> things have simple definitions that are universally agreed-upon.
>
> As for how to deal with the requriement that each state get a House  
> seat, that's a separate subject. Of course Hill, just by its own  
> rules, automatically gives a seat to every state that contains at  
> least one person. But I think that most people interpret the  
> Constitution as saying to give each state a seat, and then allocate  
> the other seats in proportion to population.
>
> By systematically favoring small states, Hill is in clear violation  
> of the Constitution.
>


When a relatively recent case reached the Supreme Court the Court  
unanimously disagreed. The mathematician who prepared the brief for  
the government was Lawrence Ernst. I thought that the briefs he  
prepared raised some interesting issues and he published his work in  
a scholarly journal afterwards. In the new edition of Balinski and  
Young's book they not only fail to comment on Ernst's paper but also  
they do not list it in their biblography. It seems to me Ernst's  
paper is worth looking at:

http://www.bls.gov/ore/abstract/st/st940450.htm


Cheers,

Joe





> Mike Ossipoff
>
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------------------------------------------------
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451

Phone: 718-262-2551 (Voicemail available)

My new email is:

malkevitch at york.cuny.edu

web page:

http://www.york.cuny.edu/~malk



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