In Defense of Gerrymandering: Politics as Usual is Better than Bad Math
Everyone knows what an unfairly gerrymandered voting district looks like, but what this post presupposes is — maybe they don’t?
Know it when you see it?
To the left are two maps of the congressional election districts used in North Carolina. Map A shows the districts used prior to the redistricting done in 2011. Map B, below, shows the current districts drawn during the 2011 redistricting process conducted by a GOP controlled state legislature — used to elect members to the 113th Congress and beyond. So which of these two is more fair?
“Knowing it when you see it” is something that you can decently well define — just compare the ratio of the perimeter to the area for each voting district. If this ratio is large, it is likely due to a legislator drawing very particular lines to incorporate or exclude very particular sets of people into a very particular district.
Above, we have graphed this perimeter-to-area ratio for each district in the 111th and the 113th Congresses. Overall, the districts used to elect members to the 113th Congress (2014) tend to be more creatively drawn.
Without any special knowledge of the situation on the ground, the perimeter-to-area ratio is probably about the best we can do — it suggests something about the potential for a region to have been ‘gerrymandered’, but it says less about the true impact on election outcomes.
But as it turns out, we do have special knowledge of the situation on the ground. For many states, and for some elections, the Harvard Election Data Archive has compiled geographically tagged datasets that provide precinct-level vote tallies. Using that data, we can create a new measure of gerrymandering — but it does require refining our definition.
How it works
Let us consider a state to be gerrymandered when, for any party, the ratio of the candidates that the party sends to Congress is misaligned with the ratio of the total statewide votes that the party receives. So we would consider a ‘fair’ districting system to be one in which if 60% of a state’s population votes for a Republican representative then about 60% of the representatives sent to Congress from that state are also Republican. If those ratios deviate significantly, then we will define the state as gerrymandered.
We then have to make an important simplification and try to normalize for differences in the individual quality of candidates — or the varying effort each party may put into each particular race — by only considering vote totals for statewide races. In this case, for example, we use a combination of straight-ticket and US Senator votes as a proxy for the general party preference of the voters in the state.
In the graphs below, we have grouped these votes in the 2008 and 2010 North Carolina elections by the two different districting schemes mapped above. From this we can simulate what congressional representation could have looked like (under the assumptions outlines above). Each grouping of bars represents a different election. Each color within that group represents a different way of dividing votes into geographic election districts. The horizontal blue line intersects the y-axis at the percentage of popular votes won by the Democratic Senate candidate (this method’s proxy for party preference). The top of each bar represents the ratio of districts won by a Democratic majority under these districting schemes.
A given districting /election scenario is less gerrymandered when the top of the column is close to the blue line.
Make No Mistake, Gerrymanders are Real
In the 2008 Senate race, shown in the left grouping of bars, the Democratic candidate won ~56% of the votes. If every voter who voted for a Democratic senator also voted for a Democratic House representative, then North Carolina would have sent eight Democrats to the House (the dark purple bar). But after the redistricting that occurred in 2011 (lighter purple bar), even with 56% of votes in their favor, the Democrats would have sent only six representatives to Washington.
The 2010 election is shown in the right hand side of the graph. Here, the Republican Senate candidate won about 54% of the popular vote. But with the districts used for the 113th Congress (2014) and the assumptions of this simulation, the Republicans would have won 77% of the congressional House seats!
When past election data is available, this is an incredibly simple way of evaluating districting schemes based on the equability of their outcomes. It demonstrates, much more tangibly than the geometric, perimeter-to-area approach, that the Republican controlled North Carolina State Legislature was incredibly effective at redrawing voting district in their party’s favor after the 2010 election.
Unbiased ≠ Fair
Many would agree that the obvious solution to such brazen gerrymandering would be to remove the politicians completely from the districting process. Some, particularly among the political technorati, advocate ‘solving’ gerrymandering using an algorithm built around a mathematically elegant allotment of population distributions. These, so the thinking goes, would create districting schemes that are objective and unbiased and fair.
Maybe.
To the left are three maps that display potential voting districts produced by these algorithms. The first is a splitline analysis put forward by the folks over at rangevoting.org and described on Vox as an example of what “America would look like without gerrymandering” (Map C). Map D is derived from the districts produced by Brian Olson’s optimal compactness algorithm — which has been often championed on Wonkblog. The last is one of my own design, wherein I took the voting precincts delineated in the Harvard Election Database and regrouped them randomly into contiguous blocks until each new block had a vote return total within the range of the original districts. This random simulation was done hundreds of times and the average electoral results were tracked. Map E is an example of the districting lines created by one of these simulations.
These algorithms produce districts with much lower perimeter-to-area ratios — districts that appear like they would result in more fair elections.
But that appearance is very, very misleading. Upon applying actual vote totals to these districting schemes we find that these algorithm-derived districts are, in essence, extremely gerrymandered.
In a world of algorithmically designed districts, when Democrats are in the majority in North Carolina, they win far more votes than they deserve. When they are in the minority, they win far fewer votes than they merit.
In both the 2008 and 2010 elections, the actual districts used by the 111th Congress (2010) in North Carolina, despite how they may look, were about as fair as you could reasonably expect from a winner takes all voting system based on contiguous geographies. I can’t say that the gerrymander crawling around the state in the years before 2011 constituted a great victory for democracy — but it was maybe the closest we’ve gotten to it in North Carolina.
If we believe proportional representation is a priority for our government, then gerrymandering should be a priority problem. Unfortunately, it appears that in this case the splitline, the optimal compactness, and my own misguided attempt at algorithmic districting all would have generated worse outcomes than our existing, corrupt political process.
Under Development:
Want me to run this analysis for your state or for your proposed districting scheme? If you have a shapefile with high resolution, precinct level vote returns or a districting scheme of your own design, email me at cwhfedor@gmail.com and I’ll crunch the numbers (and hopefully set up a fully automated system for doing this soon!)
If you are familiar with R you can try out the base code for yourself! https://github.com/raulfoo/gerry_mandarin. I have set up some demo data for Ohio in that repo as well.
The full NC datasets I used to simulate the districting vs election scenarios can be found at the link below.
Raw vote totals (without assignment to algorithmically derived districts and for races), can be found at http://projects.iq.harvard.edu/eda/home
Update: 2016/01/23
Thank you to the commenters who sent me a better definition for the geometric scoring of districts (area/perimeter^2), which is outlined below:
The new order is flipped (more ‘gerrymandered’ districts now have lower scores). This changes Optimal Compactness to fully edge out splitline and have the least ‘gerrymandered’ shape — which makes sense, since it is optimally compact... The politically drawn districts (113th and 111th Congress) handily remain the most ‘gerrymandered’ by this definition.
