[EM] More on Gerrymander prevention

Michael Rouse mrouse at cdsnet.net
Wed Mar 20 09:28:11 PST 2002

Note: this is more of a thought experiment than a serious suggestion -- the
number of states and districts is not a power of two for one thing, and
there are problems with long, skinny districts -- but it does show an
automated way of coming up with a single apportionment answer, and it might
point to a method we can agree on.

To illustrate, assume we want to break up the United States into 64 states,
or perhaps Canada and Mexico have combined with the United States to form a
North Americal Union and we want to divide the Union into 64 regions. Find
the population centroid for the country, then find the geographic centroid.
Draw the great circle that runs between them and continue until the line
reaches both borders. You now how two clearly defined sections of roughly
equal population. Find the population and geographic centroids for each of
these sections, draw another great circle line for each set, and continue
until you have 64 states (regions). Each "state" should have *roughly* equal
area and population. (I say "roughly" because of the teeter-totter effect --
a small group of people far away will balance a larger group nearby -- which
is why I have it going through the geographic centroid as well.) As an
alternative, you could use the point where the north-south population median
crosses the east-west population median, then take the line between that and
the geographic centroid. In either case, everyone who followed the
definition accurately would end up with the same result, regardless of

Instead of a power of two, we could redo the lower 48 contiguous states.
Ignoring Alask and Hawaii, cut the country in thirds -- Pacific, Atlantic,
and Central -- with equal populations, and the borders defined by longitude
lines (in other words, find the line of longitude where one third of the
population of the country is west of the line, and then find another where
one third of the population is east of the line. Those two lines will divide
the country cleanly). Within these three regions, find the population and
geographic centroids, draw lines through them, and repeat until each region
has 16 "states," giving a total of 48 states. We can keep going within these
states until each state has 8 districts, or 384 districts plus Alaska and
Hawaii, as opposed to 435 districts we have now. (We could of course do the
same thing with lines of latitude -- north, middle, and south -- and divide
each region into 16 parts, but lines of latitude are not great circles, and
the regions would be more elongated to begin with).

As mentioned above, one of the problems is that you could easily end up with
long, skinny, not-at-all-compact districts. Another problem is the districts
would completely ignore present political, historical, racial, and
geographic groupings -- it might take a thin sliver out of the center of a
city but extend far out into rural areas, and across our present state
boundries. On the other hand, each district would be a simple, closed, and
convex figure, with a near-minimum of jaggedness, and there would be only
one result possible for each census. The tesselations would also make a cool
mosaic (grin).

If the results were too strange -- districts stretching acrossed time zones
or shaped like slivers of glass -- the population centroid of each district
could be used as a "seed" result, with an algorithm moving census blocks
between districts to make each each district more compact. This would allow
some variability, but the "seeds" would limit the amount of gerrymandering

Michael Rouse
mrouse at cdsnet.net

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