Re: Population paradox

[Joseph Malkevitch]

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


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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

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