# [EM] Sainte-Lague, part 3

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Dec 5 18:33:44 PST 2006

```Did you know that Sainte-Lague, d'Hondt, and Largest Remainder were all
proposed, early in U.S. history, for apportioning the House of
Representatives? They were.

d'Hondt was Jefferson's method, Largest Remainder was Hamilton's method, and
Sainte-Lague was Webster's method (Daniel Webster).

The very first use of the Presidential Veto was when George Washington
vetoed a bill to apportion the house by LR/Hamilton. We used
d'Hondt/Jefferson for a while. 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 When that was pointed out, LR/Hamilton was immediately repealed and

At some point SL/Webster was enacted. But then, around the date of Pearl
Harbor, Congress replaced it with something new. A mathematician had begun
advocating a different apportionment method, claiming to have found
something better than the historical methods. He was opposed by someone
arguing for Webster, but the mathematician had more impressive jargon and
proofs that impressed the heck ouf of Congress. His new method is known as
Hill's method (it seems to me). It was self-flatterningly referred to as the
method of equal proportions.

Hill's method is like SL/Webster, except that it rounds off geometrically
instead of arithmetically. So a party's seat-count is rounded to the whole
number that differs by the least factor from what the quota calls for.
Instead of rounding off to the nearest seat arithmentically, as is usually
meant by "rounding off".

Hill soiunds plausible, doesen't it? After all ratio is the important thing,
and Hill puts everyone as close as possible, in ratio, to the ideal v/s.
What could be wrong with that? Starting with a Hill allocation, taking a
seat from Texas and giving it to Virginia, you could reduce the amount by
whilch those two states' v/s differ. That's what's wrong with that.

At this point, someone could say that it's a subjective matter of opinion
whether SL/Webster or Hill is more proportional. I disagree.

There's strong justification for Hare's ideal quota, and the fractional seat
allocations it calls for. But once you round that off, once you fudge it, as
SL/Webster and Hill do, you lose that justification. It's no longer solidly
obvious that you have the most proportional allocation. You've gone from
solid justification to word-games.

But SL/Webster's transfer property that I demonstrated in the previous
posting is solid justification.

I told why it means that SL/Webster is unbiased. It is easily shown that if
SL/Webster has that property, no other allocation can. And it's easily shown
that Hill favors small states, as compared to SL/Webster. Since SL Webster
is unbiased, as I showed in the previous message, then Hill must favor small
states.

We're still using Hill's method to apportion Congress. And it's probably
still called the "Method of Equal Proportions".

I'm not saying that apportionment is so important. The various methods only
differ by a seat or so. And so what if Hill favors small states. It doesn't
favor them nearly as much as the Great Compromise does. So why mention it at
all? Because apportionment has been viciously and acrimoniously fought
during U.S. history. And because pointing out that Hill is biased, and that
Webster is unbiased and optimally proportional, offers an opening into the
subject of electoral reform, which can then lead to more significant
reforms, starting with a better single-winner method.

Mike Ossipoff

_________________________________________________________________
Visit MSN Holiday Challenge for your chance to win up to \$50,000 in Holiday
cash!
http://www.msnholidaychallenge.com/default.aspx?ocid=tagline&locale=en-us

```