[EM] SL vs LR--Rounding is unavoidalbe because allocations are integer

[MIKE OSSIPOFF]

Juho--

I tried to post this a few days ago, by forwarding the "failed delivery" 
message. It didn't post, and so now I'm resending it on a different 
computer:

You spoke of Webster/Sainte-Lague having a rounding error, with the 
implication that Largest-Remainder/Hamilton doesn't have one. But rounding 
is quite unavoidable, since fractional seats can't be given (or at least are 
against the rules).

So rounding does _not_ count as a SL disadvantage in comparison to LR. SL's 
rounding. As I described earlier today, rounding makes SL a S(p) function 
that is as close as possible to a linear function. That's the definition of 
proportionality.

LR isn't a function, due to its caprice. Well ok, I've heard of random 
functions.

To answer an earlier question: LR _does_ have an additional problem, in 
addition to its nonmonotonicity: Its unnecessary random deviations from 
proportionality.

But LR is unbiased, and so I'd rather have it than Jefferson/d'Hondt. Some 
advocate d'Hondt on majority rule grounds: A party with a majority of the 
votes can't fail to win a majority of the seats. But that comes at the cost 
of bias in favor of large parties. And that brings back the old 
Lesser-of-2-evils problem: "If you vote Progresssive,  then the Progressives 
and the Democrats will get fewer votes than the Democrats would get if all 
the Progressives voted Democrat, because d'Hondt favors large parties. So 
you've got to anandon your idealism and pragmatically vote for the 
Democrats."

That sounds too familiar. I don't want an electoral reform that will retain 
that problem.

By the way, to reply to something more recent, if your party has a Hare 
quota, then it's difficult to imagine how SL could fail to give it a seat. 
In order to deny it a seat, SL would have to double the Hare quota to get 
its final quota. That would be unheard of. Adjsutments in quota size are 
quite small, to adjust the total allocation by one, or maybe two, seats. If 
your part has a Hare quota, it will get a seat. (A Hare quota is Total 
Votes/Total Seats).

Mike Ossipoff

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