<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=Content-Type content="text/html; charset=iso-8859-2">
<META content="MSHTML 6.00.2800.1106" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><FONT face=Arial size=2><FONT face="Times New Roman" size=3>There is no way
you can draw rectangles or hexagons or any other shape with<BR>automated
districting procedure. Remember, the districts have to have equal<BR>population.
You must have some certain units when you draw districts, such<BR>as street
blocks or even buildings. Whatever you use, you can never draw<BR>rectangles or
hexagons and have equal population in them. Try it and you<BR>will see it easily
that it is not possible.<BR>Several authors have produced automated districting
procedures or discuss<BR>these procedures in detail(see the literature below).
Many of these<BR>procedures do work, but none of them is based on certain type
of shape (such<BR>as rectangle).<BR>One of these automated districting models
uses established political units<BR>(such as municipalities) as districting
units and then arranges them in the<BR>districts according to the formula, under
which the difference in population<BR>is the smallest possible.<BR>Lets say we
have 50 municipalities in a state and we have to draw 4<BR>districts.
Matemathically there are many ways we can arrange these 50<BR>municipalities in
4 districts, but there is only one under which the<BR>population variance is
smallest possible.<BR>This procedure does not involve decisions of human factor,
except for the<BR>decision on the procedure used and political units used.
However, the<BR>decision on which procedure should be used will always be taken
by humans.<BR>It could be said that it was humans who drew the borders of
the<BR>municipalities (or other political units used), but these borders
have<BR>usually been drawn long ago and without intent of
gerrymandering.<BR><BR>Some literature on automated districting (mostly proposed
models):<BR>The first paper on automated redistricting is Vickrey's short, but
original<BR>and often cited 1961 article "On The Prevention Of Gerrymandering"
(sorry,<BR>at the moment I dont know exactly where it was published)<BR>Browdy,
Michelle H., Simulated Annealing: An Improved Computer Model for<BR>Political
Redistricting, Yale Law & Policy Review 8, 163-179, 1990<BR>Liittschwager,
John M., The Iowa Redistricting System, in Democratic<BR>Representation and
Apportionment: Quantitative Methods, Measures, and<BR>Criteria, New York: Annals
of the New York Academy of Sciences, 221-234,<BR>1973<BR>And a case against
automated districting:<BR>Altman, Micah, Is Automation the Answer? The
Computational Complexity of<BR>Automated Redistricting, Rutgers Computer and
Technology Law Journal 23 (1),<BR>81-142<BR><BR>Few years ago I wrote,
but never published a thesis on a subject of automated districting and if
someone is interested, let me know.<BR><BR>J.<BR><BR>>
Date: Thu, 08 Jan 2004 09:37:06 +0000<BR>> From: "MIKE
OSSIPOFF" <</FONT><A href="mailto:nkklrp@hotmail.com"><FONT
face="Times New Roman" size=3>nkklrp@hotmail.com</FONT></A><FONT
face="Times New Roman" size=3>><BR>> Subject: [EM] Automated
districting<BR>><BR>><BR>> Hexagons sounds good, till you consider that
they won't work at the<BR>borders<BR>> of the state being districted. Since
district shapes can't be hexagons at<BR>> the state's borders, why bother
making hexagons in the interior?<BR>><BR>> The populations or voting
populations in the districst of course have to<BR>be<BR>> exactly equal, or
as nearly so as possible.<BR>><BR>> The only important thing about the
districts is that they're automated and<BR>> follow from a strictly-applied
formula that has no human input, so that no<BR>> one can contrive districts
to benefit his/her political party or<BR>candidates.<BR>> They needn't be
hexagons. They needn't be made by an elaborate procedure.<BR>> Voters will
object to an elaborate procedure. There's no reason not to<BR>use<BR>>
the simplest formula possible. The formula should be as simple
as<BR>possible.<BR>><BR>> The districts should be rectangles (of course
the border-districts will<BR>lose<BR>> some of their rectangularness due to
the shape of the border).<BR>><BR>> Of course it's good if there's some
effort to make the rectangles<BR>reasonably<BR>> nearly square. But any
serious effort to achieve that will complicate the<BR>> formula. Don't worry
about how square they are.<BR>> A simple formula can make them reasonably
so.<BR>><BR>> When I say "rectangles", I don't mean that the sides must be
straight<BR>lines.<BR>> Lines of latitude and longitude would make good
district borders, even<BR>> though parallels of latitude aren't straight
lines on the ground, or on<BR>most<BR>> maps (but they are on some
maps).<BR>><BR>> Straight lines on the ground would be an unnecessarily
complicating<BR>> requirement.<BR>><BR>> Just straight lines on some
map. It doesn't matter what map. Lines of<BR>> latitude & longitude
qualify by that requirement. But any kind of map will<BR>>
do.<BR>><BR>> In fact, if one wanted to, one could use a map on which a
straight line on<BR>> the map is a straight line on the ground. Such a map
radicallly distorts<BR>> distances & areas though.<BR>><BR>> Mike
Ossipoff<BR>></FONT><BR></FONT></DIV></BODY></HTML>