# [EM] Sainte-Lague, part 3

Joseph Malkevitch malkevitch at york.cuny.edu
Wed Dec 6 18:31:05 PST 2006

```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 repealed and
>
> 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
>
>
>
>
> Send instant messages to your online friends http://
> uk.messenger.yahoo.com
> ----
> election-methods mailing list - see http://electorama.com/em for
> list info

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

Phone: 718-262-2551 (Voicemail available)

My new email is:

malkevitch at york.cuny.edu

web page:

http://www.york.cuny.edu/~malk

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