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 When that was pointed out, LR/Hamilton was immediately repealed and discarded.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 _________________________________________________________________ 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 ---- election-methods mailing list - see http://electorama.com/em for list info