Dear Election Methods,
The fact that Largest Remainder (Hamilton) violates "house
monotonicity" (e.g. Alabama Paradox) is less serious for apportioning
the US House of Representatives now that it has a fixed size of 435
than the fact that it violates "population monotonicity." (See the
book about apportionment by Balinski and Young.) All of the so-called
divisor methods are population and house monotone but can violate the
condition of obeying quota (e.g. if one takes the product of the
percent population for a state and the house size, one would like the
number of seats given to a state to be either that number if it is an
integer or the integer just larger or small than that number if it is
not an integer). The Balinski-Young Theorem basically shows that one
can not have a method that both obeys quota and is population monotone.
Cheers,
Joe
On Dec 6, 2006, at 1:58 PM, Juho wrote:
On Dec 6, 2006, at 4:33 , MIKE OSSIPOFF wrote:
There was later another bill to enact
LR/Hamilton. It passed and wasn't vetored, and LR/Hamilton was used
for a
while--till someone pointed out the bizarre paradoxes that it's
subject to:
Some people move from another staste to your state, causing your
state to
lose a seat. We add a seat to the House, and that causes your state
to lose
a seat. When that was pointed out, LR/Hamilton was immediately
repealed and
discarded. (IRVists please take note).
I understand that LR/Hamilton may lead to the Alabama paradox and
people may dislike LR/Hamilton because of this. But I think LR/
Hamilton is quite proportional and unbiased. Are there other reasons
why LR/Hamilton is not favoured? SL/Webster is close to LR/Hamilton
and avoids the Alabama paradox, but LR/Hamilton might still be
considered more exact in providing proportionality.
Juho Laatu
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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:
[EMAIL PROTECTED]
web page:
http://www.york.cuny.edu/~malk
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