[EM] Re: Automated districting

Toplak Jurij jure.toplak at uni-mb.si
Thu Jan 8 19:59:02 PST 2004

There is no way you can draw rectangles or hexagons or any other shape with
automated districting procedure. Remember, the districts have to have equal
population. You must have some certain units when you draw districts, such
as street blocks or even buildings. Whatever you use, you can never draw
rectangles or hexagons and have equal population in them. Try it and you
will see it easily that it is not possible.
Several authors have produced automated districting procedures or discuss
these procedures in detail(see the literature below). Many of these
procedures do work, but none of them is based on certain type of shape (such
as rectangle).
One of these automated districting models uses established political units
(such as municipalities) as districting units and then arranges them in the
districts according to the formula, under which the difference in population
is the smallest possible.
Lets say we have 50 municipalities in a state and we have to draw 4
districts. Matemathically there are many ways we can arrange these 50
municipalities in 4 districts, but there is only one under which the
population variance is smallest possible.
This procedure does not involve decisions of human factor, except for the
decision on the procedure used and political units used. However, the
decision on which procedure should be used will always be taken by humans.
It could be said that it was humans who drew the borders of the
municipalities (or other political units used), but these borders have
usually been drawn long ago and without intent of gerrymandering.

Some literature on automated districting (mostly proposed models):
The first paper on automated redistricting is Vickrey's short, but original
and often cited 1961 article "On The Prevention Of Gerrymandering" (sorry,
at the moment I dont know exactly where it was published)
Browdy, Michelle H., Simulated Annealing: An Improved Computer Model for
Political Redistricting, Yale Law & Policy Review 8, 163-179, 1990
Liittschwager, John M., The Iowa Redistricting System, in Democratic
Representation and Apportionment: Quantitative Methods, Measures, and
Criteria, New York: Annals of the New York Academy of Sciences, 221-234,
And a case against automated districting:
Altman, Micah, Is Automation the Answer? The Computational Complexity of
Automated Redistricting, Rutgers Computer and Technology Law Journal 23 (1),

Few years ago I wrote, but never published a thesis on a subject of automated districting and if someone is interested, let me know.


>    Date: Thu, 08 Jan 2004 09:37:06 +0000
>    From: "MIKE OSSIPOFF" <nkklrp at hotmail.com>
> Subject: [EM] Automated districting
> Hexagons sounds good, till you consider that they won't work at the
> of the state being districted. Since district shapes can't be hexagons at
> the state's borders, why bother making hexagons in the interior?
> The populations or voting populations in the districst of course have to
> exactly equal, or as nearly so as possible.
> The only important thing about the districts is that they're automated and
> follow from a strictly-applied formula that has no human input, so that no
> one can contrive districts to benefit his/her political party or
> They needn't be hexagons. They needn't be made by an elaborate procedure.
> Voters will object to an elaborate procedure.  There's no reason not to
> the simplest formula possible. The formula should be as simple as
> The districts should be rectangles (of course the border-districts will
> some of their rectangularness due to the shape of the border).
> Of course it's good if there's some effort to make the rectangles
> nearly square. But any serious effort to achieve that will complicate the
> formula. Don't worry about how square they are.
> A simple formula can make them reasonably so.
> When I say "rectangles", I don't mean that the sides must be straight
> Lines of latitude and longitude would make good district borders, even
> though parallels of latitude aren't straight lines on the ground, or on
> maps (but they are on some maps).
> Straight lines on the ground would be an unnecessarily complicating
> requirement.
> Just straight lines on some map. It doesn't matter what map. Lines of
> latitude & longitude qualify by that requirement. But any kind of map will
> do.
> In fact, if one wanted to, one could use a map on which a straight line on
> the map is a straight line on the ground. Such a map radicallly distorts
> distances & areas though.
> Mike Ossipoff
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