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
