05 May, 2005

An analysis of gerrymandering in U.S. Congressional districts

An interesting quirk of our democracy is that legislatures must reapportion the boundaries of voting districts at regular intervals. This gives the representative considerable power to decide his or her own fate, since they can effectively choose the electoral body that they will "represent". For example, Congressman Black might prefer a district that includes mostly poor minorities, while Congresswoman White would like her district to include the fru-fru, quiche-eating country club types. This can be a mutually beneficial relationship; incumbency is paramount. To the detriment of democracy, since representatives are thus secure, with a consolidated base, and are free to pursue all sorts of dastardly corruption without fear of being unseated or even significantly challenged.

Thus, my motivation for this analysis of gerrymandering of U.S. Congressional districts. "Gerrymander" originated from one Elbridge Gerry, of Massachusetts, who redrew his district so that it resembled a salamander, slithering across the state.

My assumption was this: a non-gerrymandered (GM) district will have a simple shape, like a square or a circle. A GM district, on the other hand, will be oblong and spidery (like Florida's District 22, to the right). A simple metric to capture this difference is the ratio of the area to the square of the perimeter of the district.

Some notes on methodology:
My data set was the 108th Congressional districts, taken from the U.S. census website.Unfortunately there are no maps available for the 109th Congress as of yet. I then identified the region within the district via a few image filters (basically, identifying the border by color and flood-filling it). Most of this could be done computationally; a few (~10) were too complex and required a modest amount of hand-editing.

A notable difficulty is coastlines. First, because district boundaries often extend way off into the water (as with my own), simply for map-drawing convenience), the shape of the district may not accurately reflect its electoral range. That is, there is no reason to include empty water as either area or perimeter, since it could obviously not serve as motivation for gerrymandering. But, second, coastlines have fractal geometries and highly intricate borders, and if I merely subtract away all the water from the district, this leaves an artificially complicated border with an enormous perimeter. A compromise is to subtract water that is far away from land, but count it when it is close to land (effectively smoothing out the coast).

I was not totally meticulous about checking my results, but the method went through three iterations over its development (the past few days, between doing ACTUAL work), and I believe it's roughly error-free, and about as indicative as this simple metric can be. I hope the results speak for their own accuracy.

Since your appetite is now hopefully whetted, here are some results.

Average gerrymandering by state. I've arbitrarily multiplied my score by 1000 to make it more readable; you can catch number of districts in the state as well. I've color-coded by partisan status (based on Congressperson).
MD 6.88793880535598 8
GA 8.50851723977752 13
VA 8.98535082698503 11
WV 9.30040737254421 3
NC 9.68898361365534 13
MA 9.83815278770039 10
RI 10.3367699156752 2
AK 10.4485686714127 1
CA 11.1569187555363 53
PA 11.2178984267845 19
NY 11.3708290869881 29
TN 11.5855566566526 9
NJ 12.0420686498261 13
NH 12.1578267933015 2
LA 12.2445438938043 7
AL 12.4107845305385 7
ME 12.4741193904276 2
SC 12.6619477973961 6
IL 13.1024810826366 19
FL 13.6986245130043 24
TX 14.5563881134424 32
WA 14.5889054246271 9
CT 14.7686056184507 5
OH 16.1212612375961 18
KY 16.4950727687108 6
MO 16.5901389002228 9
NV 16.9636163319575 3
OK 17.0302256381007 5
DE 17.9639557785057 1
MS 18.4056015269158 4
AR 18.6930775427076 4
IN 19.0298976932724 9
ID 19.0611097181691 2
CO 19.190015615601 7
MN 19.668740404658 8
OR 19.8991234034763 5
MI 21.3541582563898 15
AZ 22.1584468774782 8
WI 22.1993707024622 8
IA 23.3256579617634 5
UT 25.1600292963252 3
VT 25.1601919520778 1
NE 25.182095595885 3
NM 25.6531361363256 3
KS 26.0170276559194 4
MT 36.2821268787846 1
HI 39.8850037043964 2
SD 41.9751521430988 1
ND 47.6133854255138 1
WY 53.3433982895139 1

Here's the 15 worst districts in the country. You'll note that it's heavily biased towards Democrats. This is representative; of the top 150 GM districts, 100 are Democrat.

CA_23 2.15392705251479 249613419Capps, LoisD
FL_20 3.41104498269896 425061612Deutsch,PeterD
FL_22 1.74145540968764 376024620Shaw, E. Clay Jr.R
GA_08 2.19182084493442 626486002Collins, MacR
GA_11 2.82575367189675 453858192Gingrey, PhilR
GA_13 2.15803292714407 490451899Scott, DavidD
MD_02 1.94030760534665 602470411Ruppersberger, C. A. DutchD
NC_03 2.41473482901921 578680840Jones, Walter B.R
NC_12 2.24523848405671398435637Watt, Melvin L.D
NJ_06 2.86701555517374 419850526Pallone, Frank Jr.D
NJ_13 3.44740247443505 356043691Menendez, RobertD
NY_08 2.54177448357528 302023182Nadler, JerroldD
NY_09 2.98325633510843 365239788Weiner, Anthony D.D
PA_01 3.26930653336639 411455333Brady, Robert A.D
PA_12 3.35095973846017 509086817Murtha, John P.D

And here's the raw data.


i can't believe you did all that! can i see your code?

your methods seem to estimate higher gerrymandering for small states. what do you think that means? (and does it make any sense for states with one representative?)

it also seems open to question whether districts should follow population boundaries; historically that's been the case, which might account for weirdly-shaped boundaries (howveer you define that) w/o it actually being gerrymandering.

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