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
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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:[EMAIL PROTECTED]] Sent: Tuesday, February 04, 2003 7:57 PM
To: [EMAIL PROTECTED]; [EMAIL PROTECTED]
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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