[EM] Reposted - New measure of population density fairness for judging proportional fairness of redistricting plans

[Kathy Dopp]

On Sat, Oct 22, 2011 at 8:35 AM, Jameson Quinn <jameson.quinn at gmail.com> wrote:
> I have looked further at the PDF measure, and I've found a more-serious
> problem.
> Using your examples, imagine that the central city, instead of containing 60
> Democrats, contains a homogeneous mix of 40 Democrats and 20 Republicans.
> Thus, the state as a whole contains 60 Republicans and 40 Democrats, but the
> rural areas are intrinsically more partisan (R) than the urban areas (D).
> (This is actually unlike the real conditions in many states, which have
> strongly-democratic inner cities and weakly-republican rural areas; but the
> flaw I'm pointing out would still hold if you shrink the city and make it
> the more partisan group.)
> Now, the pie-wedge districting is still biased in favor of the majority
> party (Republicans in this case). But the hamburger-bun districting is
> proportionally fair, while the pac-man districting (favored by the PDF
> measure) is not.
> I don't see how any nonpartisan measure like PDF could possibly favor the
> pac-man when partisanship is evenhanded, but favor the hamburger bun when
> partisanship is unbalanced.

Except I think which party tends to be favored depends upon the
direction of imbalance of the partisanship levels. It would be nice to
have  actual data to play with. Your example showed the partisan
imbalance to be weighted to the rural areas and Republicans which as
you point out, is not the current situation.

Yes. I see what you mean. I tended to think about the existing
situation today in most states when I derived the PDF measure, which
may not always be the case.


> Since in the real world, except in 2 "reddest"
> states [1], Democratic strongholds tend to be more highly-partisan than
> Republican ones, I believe that the PDF would systematically favor
> Republicans;
> though perhaps less so than some other partisan-blind systems.

I think the PDF would systematically favor Democrats, due to the fact,
as you note, that urban areas today tend to have higher partisanship
levels than rural. The current use of area compactness favors
Republicans, which I was trying to correct.

> I consider this to be a serious, possibly a fatal, flaw.

Yes. While the current form of my PDF measure makes representation
proportional for the balance of regions having diverse population
densities, you are right that if the slope of the level of
partisanship is dissimilar to the slope of the level of population
density, then it won't be a perfect measure.

I agree with you that this flaw (that partisanship levels may not vary
strictly linearly with population density) cannot be overcome using a
nonpartisan measure.

Of course the same measure could be based solely on a weighted balance
of district partisanship and so blatantly ensure a proportional
partisan balance, but partisanship always varies at least slightly
during the ten years of a district's lifetime, so that would be
similar to using population compactness, rather than area compactness,
to draw districts.

Great point Jameson.

However, the PDF measure still balances the representation among urban
and rural districts very nicely and will tend, in today's situation of
population distribution to balance the partisan representation.

I'll go back to my spreadsheet and input the partisanship variable to
do further testing.

Thanks.

Kathy

http://electionmathematics.org
Town of Colonie, NY 12304
"One of the best ways to keep any conversation civil is to support the
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Fundamentals of Verifiable Elections
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