[EM] Sainte-Lague, part 3

[MIKE OSSIPOFF]

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 When that was pointed out, LR/Hamilton was immediately repealed and 
discarded. (IRVists please take note).

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

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