FYI, This is pretty exciting stuff re. redistricting. I've been working for the last several weeks on this and believe I may have derived a new, and fairly simple, nonpartisan, objective measure for evaluating how proportionately fair redistricting plans are in terms of their representation of various regions differing in population density. Since partisanship usually varies with population density, this measure would tend to ensure the partisan fairness of redistricting plans.
Legislative Redistricting - Area and Population Compactness and Population Density Distribution Measures http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1945879 This article discusses three measures proposed to evaluate the fairness and convenience of redistricting plans: (1) Area compactness, (2) population compactness, and (3) a new population density fairness measure. There are over a dozen proposed competing measures of area compactness. Pictorial counterexamples demonstrate how most of these measures are unreliable. This article argues that area compactness is reliably measured using any of the area-to-square-of-perimeter measures (or their reciprocals or square roots) because all such measures rank any two redistricting plans in exactly the same order. The isoperimetric quotient is recommended because it has a maximum value of one (1) when the district is as compact as a circle, a minimum value approaching zero, and enables direct comparison of any two districts’ compactness regardless of size. On the other hand, population compactness helps to ensure districts are convenient for voters and politicians. Population compactness can be measured using the distance of a district’s census blocks, weighted by its proportion of the district’s population to the district’s population centroid. However, due to unequal population distribution patterns, neither area nor population compactness guarantee proportionally fair representation. To measure whether a plan is proportionately fair for both urban and rural dwellers representation this article introduces an objective, nonpartisan population density fairness (PDF) measure for evaluating when a plan produces legislative representation approximately proportional to its relative numbers of urban and city dwellers. In other words, this paper proposes a measure for evaluating proportional representational fairness of legislative redistricting plans for regions having diverse population densities. -- 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 -- 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