[EM] IIAC. Juho: Census re-districting instead of PR for allocating seats to districts.

[Michael Ossipoff]

Juho--

You said:

Can you give an example where there is a difference between those
methods? (Sainte-Lague and Largest-Remainder)

Yes, in the sources that I've already referred you to. Do you really
need me to look it up for you? I will again refer you to the sources
that I referred you to before:

1. _Fair Representation_, by Balinski & Young (a book that is found in
most university libraries)

2. My PR articles at the barnsdle electoral website. At that website
is an article demonstrating that Sainte-Lague is the optimally
proportional method.

Balinski & Young's book is about apportionment methods for the U.S.
House of Representatives. Nearly all of the European PR methods, all
of the main ones, were proposed and used to apportion the House of
Representatives at one time or another.

Sainte-Lague is called "Webster's method" for House apportionment.

Largest-Remainder is called "Hamilton's method" for house apportionment.

> You talk about "differences in district representation per person". Does that refer to the Alabama paradox that causes movements up and down when > the number of seats changes, or do you refer to changes in population/voters or in number of districts?

Neither. As I said before, Largest-Remainder, though unbiased,  is
subject to random errors, fluctuations in its allocations that result
in deviations from proportionality that are greater than those of
Sainte-Lague.

I wasn't referring to LR's paradoxes. Certainly they're undesirable,
especially since they're avoidable in a party list system. But no,
they aren't what I was referring to. I was referring to unbiased but
consistently-present deviations from proportionality that are greater
than those of Sainte-Lague.

You spoke above of Largest-Remainder's advantages. Name one.Explaining
the method briefly to someone who isn't interested in PR? When I was
discussing PR, I used to define and explain Sainte-Lague briefly.
Largest Remainder has the very inelegant and unaesthetic quality of
being a combination of two different successively-applied rules: One
that is proportional, and then one that takes leave of
proportionality.

I don't criticize you when you say that you prefer LR because of its
historical use. But saying that it has advantages is a whole other
matter.If it has an advantage, then what is its advantage?

>
> If you talked about fair allocation of seats to small districts, here's one possible example. Largest Remainder gives the first seat (out of 10 seats) to the second group with proportions 93-4-3. In Sainte-Laguë we need 93-5-2. What is your definition of ideal fair allocation? Should small parties be favoured more or less?

If  optimal proportionality is the goal, then small parties should be
favored less when to favor them more would create a greater deviation
from proportionality. Of course neither Sainte-Lague nor
Largest-Remainder consistently favor or disfavor small parties or
large parties. Both are size neutral, size unbiased.

Sainte-Lague/Webster minimizes differences in seats per person.
Starting with a Sainte-Lague seat allocation to districts, take a seat
from one district and give it to another. That will always result in a
greater difference between those two districts' seats per person.

But, to answer your question in another way, it's purely a matter of
opinion whether small parties should be favored less. Remember that I
don't advocate PR for the U.S. . I'd rather exclude parties that
aren't liked enough to in in a single-winner election. That would
favor small parties less.So, for the U.S. Congress, my answer is yes,
small parties should be favored less. (But don't be so sure which
parties will or won't be able to win here in single-winner elections
with an adequate voting system).

That said I have nothing against PR. I'm not telling Europeans that
they shouldn't use it. They have a fine system. It just isn't my
_favorite_ one to propose here. As I said, if the choice were to keep
Plurality or immediately change to European PR, I'd vote "Yes" on that
proposal without any hesitation.

And, as I also have already said, PR is entirely out of the question
here, because it would be a completely different system, a whole new
concept and approach to representation. Single-winner reform, in
contradistinction, is just a better way of doing what we already do:
electing candidates in single-winner elections.

> Is Sainte-Laguë's seat allocation 1-1-1 with proportions 57-23-20 ok? Note that this introduces an incentive to split a minority district (43) in two parts (23-20) to get majority of the seats. (may lead to gerrymandering)

Nothing will lead to gerrymandering if an un-gerrylmanderable
districting system is used--an automatic districting rule that allows
no human input.

Shortest-Splitline and Band-Rectangle are both good.
Shortest-Splitline has a briefer definition. Band-Rectangle is a lot
easier to implement. It uses far less computing time. In fact it
doesn't even need a computer.  Remember that districting was done long
before there were any computers. There's nothing about Band-Rectangle
that would prevent it from being done by the people who drew districts
long before there were computers.

But if you're claiming that there are examples of a
splitting-incentive in Sainte-Lague, but not in Largest-Remainder,
then you should say so. It seems to me that I read that d'Hondt is the
method that avoids any splitting-incentive, and that d'Hondt is the
method that guarantees that a majority of the voters will elect a
majority of the seats.

Find and read Balinski & Young's book.

Mike Ossipoff