# [EM] More on Gerrymander prevention

Michael Rouse mrouse at cdsnet.net
Sun Mar 24 08:44:56 PST 2002

```After surfing the web for information on how to divide maps without
gerrymandering, I think I found a standard that won't offend most people.

The ideal district under most standards has the following features:
1. Equal Population
2. Contiguous
3. Compact

If we were to define the ideal districting map to be a centroidal Voronoi
diagram where each Thiessen polygon has the same number of people, then the
map that comes closest to this standard should be the one we choose. (See
http://www.math.iastate.edu/gunzburg/voronoi.html#quan and
http://www.cs.ubc.ca/~ajsecord/npar2002/html/stipples-node2.html for
examples -- phrases like "Voronoi diagram" and "Thiessen polygon" look
impressive, but the ideas behind them are easy to understand.)

In practice, we would say something like "The districting map of the
(country, state, county, city) shall be a Voronoi tessellation where each
polygon contains equal (population, citizens, adults, voters) and the
cumulative distance between Voronoi generators and Voronoi centroids is
minimized."

By their nature, these polygons are contiguous and compact -- they are also
convex, simply shaped, and just look nice (which may not seem important, but
federal judges view gerrymandering as they do pornography -- "They  know it
when they see it"). Just as important is having the ability to compare two
or more competing plans with a set standard, and allowing interested
citizens and groups of citizens to offer their own plans. On the down side,
these polygons ignore roads, rivers, and ridges, communities, city limits
and county lines, etc. And while they are easy to calculate for most states,
states like New York, Florida, Texas, and *especially* California might be
looking at a problem that is impossible to solve exactly -- and
redistricting an entire country (not necessarily the U.S.), we would have to
settle for "excellent" rather than "perfect" districting.

Still, "excellent" is better than the "godawful" method we have now.

Michael Rouse
mrouse at cdsnet.net

```