[EM] Oops! I should stick with single-winner methods

[MIKE OSSIPOFF]

For nearly all of my time on this list, I've said that I specialize in 
single-winner methods, and I refused to discuss PR. Well, I definitely 
should stick to that policy!

I felt safe repeating what I said 18 years ago, when I was into PR, but it 
turns out that I seem to have made a few mis-statements even then, about 
Sainte-Lague's transfer property.

It now seems to me that, in SL/Webster, a seat transfer will always increase 
the _difference_ in their seats per vote (or seats per citizen, in 
apportionment). And that, in Hill, it will always increase the ratio by 
which their seats/vote differ. That's contrary to what I've been saying 
here, because I've been claiming that Hill can't have a transfer property.

Which is more important? Say I reside in Texas, and you reside in Kentucky. 
Should your and my individual seat-fraction (seats per person) have minimum 
difference with respect to seat-transfers between our states, or should it 
differ by minimum ratio with respect to those seat transfers?

I think it sounds fairer to minimize the difference between our seats per 
person, rather than the ratio. If without the transfer my s/p is greater 
than yours by more than yours would be greater than mine with the transfer; 
and if without the transfer your s/p would be higher than mine by a greater 
_factor_ than it would be without the transfer, then the transfer should be 
done, because we want to minimize how much more House voting power one 
person has than another person.

But, as for bias or unbias, I now have to admit that I haven't demonstrated 
anything about that.
If a state's ideal allocation (before rounding) has a flat probability 
disrtribution then Webster is unbiased and Hill favors small states. But I 
wouldn't know what to say about the distribution.

But Balinski & Young say and demonstrate that Sainte-Lague Webser is the 
unbiased monotonic method, and so I feel safe repeating that.

Now, all this might be garbage, just like my previous transfer-property 
statements. As I said, I'm going to limit my electoral method discussion to 
single-winner methods. Even that discussion is temporary for me, though I 
might comment on a few more postings before I quit again.

I hoped to post these retractions before someone else pointed out my errors, 
but apparently two people beat me to it :-(  Well, at least I'm posting this 
before reading where they point out what an ass I've made of myself :-)

Mike Ossipoff

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