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

[Jameson Quinn]

Mostly I agree with you. One small quibble:

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.


This flaw is that one-sided partisanship may not be *proportional* with
ordinal population density. The idea that partisanship may not even be *
linear* with population density (ordinal or cardinal) is a totally separate
flaw; one which I'd mentioned and provisionally discounted as insignificant
(as long as plans are also reasonably compact) in my earlier message.


> 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.
>

This sounds plausible to me, but it would be great if you had evidence. Can
you run the PDF numbers for existing proportional, compact, pro-Democrat,
and pro-Republican filibuster proposals for a representative state (such as
FL)? I know that that's not a trivial project at all, but it would make your
paper truly fascinating.

Jameson


> 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
> 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
>
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