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

[Kathy Dopp]

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

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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