Population paradox

Joseph Malkevitch joeyc at CUNYVM.CUNY.EDU
Tue Feb 4 16:56:54 PST 2003

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 



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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