A GIS analysis of Gerrymandering compared to OPRA

I ran across a very interesting blog post by a creative GIS specialist named Blake Harvey, on his Geo Ideas blog. In it, he proposed a formula for measuring gerrymandering, and he proposed this ranking for states based on his formula:


Map scraped from Blake Harvey’s Geo Ideas blog post

The formula Blake used for his Gerrymander Index compares in one interesting respect to OPRA’s formula, but it also differs in an important way.  Blake’s GI is calculated as  (100 * 4π * Area) / (Perimeter * 2).  This “rewards” states for districts that most closely approximate circles, which makes intuitive sense.  But interestingly, the Area within a state doesn’t change, so the only real way for a state to reduce its GI is to reduce the total Perimeter of its district boundaries, which is exactly what OPRA focuses on: the districting scheme with the lowest total Perimeter for district boundaries in a state is the winner.

Now, here’s the important difference between Blake’s GI and OPRA: Blake is including interstate boundaries and coastlines in his Perimeter calculation, which (as he himself points out) gives the counter-intuitive result that Alaska, which only has one House representative, comes out in the top tier of most gerrymandered states because of its extraordinarily long and convoluted coastline. OPRA effectively ignores interstate and coastal boundaries because it is looking for the lowest possible perimeter whether these boundary conditions are included or not.  (On the other hand, OPRA would not be useful for comparing gerrymandering between different states, only in comparing schemes within a state.)

But taking both the similarity and difference into account, it is interesting to assess what Blake’s results might tell us about redistricting if OPRA were widely adopted.

First, Blake’s grand prize winner for gerrymandering is North Carolina’s painfully contorted 12th district, the subject of much attention including my most recent blog post.

Second, one is drawn to the ten red-colored states, identified as the worst offenders.  Let’s give Alaska, Maryland and New Jersey a quick pass due to the preponderance of their complex coastlines and focus on the other seven.  All of these seven states’ statehouses (governor and legislature) are controlled by one political party, all Republican, with the sole exception of Virginia which has a Republican governor but whose legislature is split between Democrats in the lower chamber and Republicans in the upper chamber*. These states contain 22% of the total US population that is represented in Congress, but also sent to Congress almost a third of the Suicide Caucus who drove the government to its recent shutdown (31.2%) and the dead-enders who ultimately even voted against the final House/Senate compromise that avoided default on our sovereign debt (32.9%).  So you have state one-party control, corresponding with a high degree of political latitude in drawing gerrymandered districts, contributing disproportionately to hyper-partisan silliness and gridlock in Washington.

Finally, I think it is interesting to look at Blake’s green winners among the states that have more than one representative: New Mexico, Nebraska and Kansas.  New Mexico’s plan, with a dense core around the urban areas and efficient “lightning strike” boundaries to the borders, looks intriguingly similar to a likely OPRA-winning approach I described here.  Kansas and Nebraska seem on the surface to be potential OPRA winners, with compact districts in more urban areas but with radial districts that may be more efficient than trying to bisect the length of the state.

And how did these district boundaries come about? Nebraska has a Republican governor but a unicameral legislature selected in non-partisan elections.  New Mexico is split with a Republican governor and Democratic legislature and Kansas is Republican-controlled, but due to legislative infighting (in Kansas’s case because Republicans couldn’t agree on how best to keep Democrats out of the House) both of these state’s districts were ultimately drawn by a federal judge.

*Even in Virginia, the Republicans in the upper chamber pushed through the latest redistricting scheme without a single Democratic vote. 

About noahkennedy

non-fiction author
This entry was posted in Boundary mathematics, north carolina, OPRA, Politics of Redistricting and tagged , , . Bookmark the permalink.

2 Responses to A GIS analysis of Gerrymandering compared to OPRA

  1. Pingback: Hands-Off Redistricting and Minority Voices | Fair and Sane Redistricting

  2. NJ says:

    In order for the GI to be 100 for a perfect circle, shouldnt the formula be 100*4*pi*area/p^2?

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