Population paradox

[Joseph Malkevitch]

Dear Josh,

If one looks at the censuses since 1890 when Montana was admitted to the 
union you will see that sometimes Huntington-Hill gave it more seats 
than it deserved and sometimes fewer. Bias over time might be due to the 
constitutional restriction of at least one seat for every state and bias 
due to the effects of the method itself.

Regards,

Joe


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


Phone: 718-262-2551
Web page: http://www.york.cuny.edu/~malk


> A bias over time for small states?
> 
> I think they are entirely incorrect.
> 
> Over time, half the small states will have an advantage, half will be at a
> disadvantage.
> 
> example today:
> Average district: 660K
> 
> Wyoming: 490K (-170K)
> Montana: 905L (+245K)
> 
> The way things are going, Montana will _NEVER_ get a second seat.
> 
> The 7 single district states are...
> 
> 
> Alaska   628K
> Delaware 758K
> Montana  905K
> N. Dak   644K
> S. Dak   756K
> Vermont  610K
> Wyoming  495K
> 
> Total = 4.796M
> 
> Divided by 66OK = 7.2 seats. (the actual average district size, if anything
> is smaller, but 660K is fair)
> 
> So, for the next 10 years, the 7 single district states are _under_
> represented.
> 
> If you throw in D.C (519K, non-voting member, doesn't count) it gets back to
> about average.
> 
> The same held true for the last census (actually, it was slightly worse for
> the smallest states last time)
> 
> Maybe someday I'll get the relevant section of the congressional record
> online.
> 
> ciao for now
> 
> 
>> -----Original Message-----
>> From: Joseph Malkevitch [mailto:joeyc at CUNYVM.CUNY.EDU] 
>> Sent: Tuesday, February 04, 2003 7:57 PM
>> To: election-methods-list at eskimo.com; joeyc at CUNYVM.CUNY.EDU
>> Subject: Re: Population paradox
>> 
>> 
>> Dear Readers,
>> 
>> Like deciding what election method is "best" or "fairest" there are 
>> similar difficulties for apportionment. There are 
>> mathematical theorems 
>> which state that among "divisor" methods, for each of the 5 methods 
>> traditionally considered (Jefferson, Adams, Webster, Huntington-Hill, 
>> Dean), there are optimization functions that each of the 
>> methods is best 
>> for. However, none of these methods guarantees that a state 
>> is given its 
>> "quota" or its quota plus 1. The argument against Huntington-Hill by 
>> Balinski and Young (they favor Webster) is made on the basis of bias 
>> over a period of time in using this method towards small states. 
>> However, one can argue that bias can occur due the constitutional 
>> requirement that every state no matter how small in population get at 
>> least 1 seat, and bias due to the method itself. It's not 
>> clear to me at 
>> least how to sort out these two factors (see paper by 
>> Lawrence Ernst). 
>> Also, if one believes that relative error is more important than 
>> absolute error, and bias need not worry one, then one can support 
>> Huntington-Hill.
>> 
>> Cheers,
>> 
>> Joe
>> 
>> 
>> -- 
>> Joseph Malkevitch
>> Department of Mathematics
>> York College (CUNY)
>> Jamaica, New York 11451
>> 
>> 
>> Phone: 718-262-2551
>> Web page: http://www.york.cuny.edu/~malk
>> 
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>> FAQ, etc), 
>> please see http://www.eskimo.com/~robla/em
>> 
>> 
> 
> 
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