[EM] Fix Philly Districts (Warren Smith)

[Kathy Dopp]

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 <warren.wds at gmail.com>
>
>    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