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

[Jameson Quinn]

I like your PDF a lot. You could also use the same idea to measure
minority/majority fairness for a given ethnicity (but probably not more than
one, without getting into the problem of optimizing on too many dimensions).
The problems I see:

1. If the measure being equalized (population density or minority status)
was too highly correlated with partisan status, it would tend make too many
uncompetitive "safe seats". This could in principle be mitigated by
statewide rules which reduced the advantage of incumbency in the party
primaries... but I don't trust that to happen. Still, safe seats are on the
whole less of a problem, in my view, than nonproportional gerrymandering; so
I'd be willing to accept this price.

2. If the partisan/population density relationship was not linear, a clever
gerrymander could take advantage of that fact. I doubt this would be
possible without ruining compactness, though, so again, not too huge a
problem.

3. It's not as good as a good proportional representation system. But it's a
far less radical change which doesn't pretend to be. So this is not really a
criticism; more just a comment.

Jameson

2011/10/20 Kathy Dopp <kathy.dopp at gmail.com>

> 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
>
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