Warren, I am fairly certain that you made a logic error by conflating the Roeck and Schwartzberg methods, which I believe are not equivalent. http://rangevoting.org/TheorDistrict.html
In fact, the Schwartzberg method seems to me to be equivalent to the class of compactness measures which use the ratios of perimeter to area (or better yet, the ratios of perimeter squared to area or alternatively, perimeter to square root of area). All such methods, including Schwartzberg's method, validly measure area compactness in a way that is not susceptible to gerrymandering (wiggly boundaries does decrease measured compactness values) and does not have the tendency you claim when you say: "these three ideas – and many others – are stupid, is that you can take a multi-district map "optimal" by this measure, then add a ton of essentially arbitrary wiggles to large portions of the district boundaries, while leaving the "quality" of that map exactly the same" I believe you are correct in making that claim for the other measures you discuss on your web page, but not for the Schwartzberg method. I have done a mathematical proof that this class (using ratios of powers of perimeter to area of the districts) of compactness measures are equivalent in the sense that they rank any two redistricting plans in exactly the same order. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1857944 I cannot recall currently why I abandoned the idea of minimizing the sum of perimeters of the districts. If I recall I will let you know. That is not to say that your split-line algorithm is not a useful approach to finding the most compact set of districts, although there are other concerns with drawing districts in addition to population, including political and geographic boundaries, including election jurisdiction boundaries in order to make the districts convenient to serve, comprehensible to voters, and convenient to administer. I wonder if you could adjust your splitline algorithm to take those other factors into account, and then use the isoperimetric quotient (the most logical measure to adopt of the class of equivalent compactness measures) to evaluate any two of the redistricting plans your splitline algorithm finds are adjusting to minimize the number of independently administered jurisdictions within each district and take account of impassible mountain ranges and rivers that divide communities. Many people claim keeping communities together is very important in redistricting. > Date: Wed, 7 Sep 2011 12:36:18 -0400 > From: Warren Smith <[email protected]> > > https://www.fixphillydistricts.com > > They held another district-drawing contest. $500 prize. > While the winning plan(s) seem to improve over the old ones, they > don't strike me as > ultra-wonderful. It seems plausible splitline or Olson would have done > comparably or better. > > I noticed they mentioned only the Roeck and Schwartzberg compactness > measures for districts, > which both were flagged in my review as stupid and > incredibly-ultra-stupid measures, respectively: > http://rangevoting.org/TheorDistrict.html > > > -- > Warren D. Smith > http://RangeVoting.org? <-- add your endorsement (by clicking > "endorse" as 1st step) > and > math.temple.edu/~wds/homepage/works.html > -- 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
