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

[Jameson Quinn]

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

Jameson

[1] OK and WY; see
http://www.bostonreview.net/BR36.5/jonathan_rodden_jowei_chen_congressional_redistricting.php

2011/10/21 Kathy Dopp <kathy.dopp at gmail.com>

> Newly posted so people can read it since it is currently unavailable
> on the ssrn.com site.  Warren's analysis of it he posted to this list
> was off-base. The simple formula cannot be simplified further, like
> Warren did, by removing all measures of district and state densities,
> removing the weights, removing the square root, claiming a^2+b^2= a+b
> etc. To obliterate my PDF measure algebraically causes my measure of
> proportional fairness of redistricting plans to be nonsensical - of
> course - as Warren happily discovered. I spent three days this week
> working to simplify the algebraic expression for PDF to its absolute
> simplest form after deriving it in a very complex way first. It can
> not be further simplified, although its form could be altered.
> However, I think its current form is good.
>
> Legislative Redistricting - Area and Population Compactness and
> Population Density Distribution Measures
>
>
> http://electionmathematics.org/em-redistricting/LegislativeRedistricting2.pdf
>
> -------
>
> My new PDF population density fairness plan measure was derived to
> make single-member districting plans proportionately fair - on the
> state level - for political parties that are distributed according to
> population density as the Republican and Democratic parties in the US
> tend to be. However, the PDF measure could be altered to measure the
> proportional fairness of plans according to other available
> demographic variables as well.
>
>
>
> --
>
> Kathy Dopp
> http://electionmathematics.org
> Town of Colonie, NY 12304
> "One of the best ways to keep any conversation civil is to support the
> discussion with true facts."
> "Renewable energy is homeland security."
>
> Fundamentals of Verifiable Elections
> http://kathydopp.com/wordpress/?p=174
>
> View some of my research on my SSRN Author page:
> http://ssrn.com/author=1451051
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>
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