On Sat, Oct 22, 2011 at 8:35 AM, Jameson Quinn <[email protected]> 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 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
