# [EM] Redistricting Paper w/ New Population Density Fairness (PDF) measure

Kathy Dopp kathy.dopp at gmail.com
Thu Oct 20 12:42:13 PDT 2011

```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

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
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
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.

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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

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