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

[Michael Ossipoff]

Juho--

Kristofer is right. I was unfair to SL when I said that it doesn't have an
optimization, that it isn't optimal in some way. Here is its important
optimization:

SL puts every district as close as possible to its correct proportional
share.

What do I mean by correct proportional share? Divide each district's
population by the same divisor. The (usually non-integer) quotients for
each district are their proportional share. These proportional shares of
course depend on what the divisor is. The divisor of course is chosen so
that, when the quotients, the correct proportional shares, are rounded to
the nearest integer, the desired number of seats will result.

We're more used to the Hare quota being the divisor, but it has no special
status for the purpose of finding correct proportional shares. Any divisor
will do.

Divide each district's population by the same number, and the result will
be exactly proportional to the districts' populations. Hence my term
"correct proportional share".

Putting every district's seats as close as possible to its correct
proportional share is an important and meaningful optimization.

Ideally, I'd like to minimize the maximum difference among the districts'
S/Q. But that probably requires a calculation-intensive trial and error
procedure. SL's optimization, the one that I described above is important
because it say something about _each_ district. When each district is as
close as possible to its correct proportional share, no district can be
seriously shorted, and the allocation is optimized in an important
meaningful way.

But you're right, Juho, we must agree to disagree.

Here is what me must agree to disagree on: The matter of whether or not
people have a right to equal representation.

Your criterion that you mention in your post sounds suspiciously like the
definition of LR.

When you enforce it, be sure to ask the people to whom you give
drastically, unnecessarily less representation per person if that's ok with
them.

Kristofer:

The important SL  seats/person optimization, it seems to me, is the one
that I described above.

The minimum variance that you spoke of sounds good, but it's a _global_
property. The optimization that I described above is something that SL does
for each party.

Anyway, we agree that SL is the best choice for equal s/q, and therefore
the best district apportionment choice. And the best PR, if equal s/q is
the goal. Unless someone wanted to do the more computation intensive trial
and error process to minimize the greatest difference any pair of
districts' s/q.

Mike Ossipoff





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