America’s political geography makes defining an algorithm that doesn’t disenfranchise voters incredibly difficult.

For some time now, computer scientists have been trying to eliminate corruption in the U.S. Congressional redistricting process by passing on the decision-making to computers. Ideally, if a computer could auto-generate boundary lines based on predefined algorithms and updated census numbers, the dark art of gerrymandering would be completely eliminated. No longer would politicians be able to choose their constituents rather than the other way around. States would be divided into equally populous regions according to pre-defined algorithms, and politicians would have no control over the outcome. Complex software programs like Maptitude, Red­Appl, and autoBound are already being used to design and gerrymander districts. So why not let them fully automate the process?

Algorithmic redistricting appears ideal in vision, but it is almost impossible in practice. At its most basic, drawing equally populous regions should be a very solvable problem. A simple splitline algorithm can repeatedly halve a state into subdivisions until the optimum population-per-area is achieved.

The problem is that districts need to be more than equally populous. Proposition 5 of the Voting Rights Act, which is being debated in the Supreme Court this week, requires that states may not deprive minority voters of the opportunity to "elect representatives of their choice." It’s for this reason that some Southern states are still required to have their redistricting plans approved by the Department of Justice so that their boundary lines do not gerrymander minority groups completely out of representation.

The historical example of this is the 1973 redistricting plan for Hinds County, Mississippi. Officials there were able to devise a county-dividing algorithm that would equalize population, land area, county road mileage, and number of bridges. Egalitarian and simple on the surface, the resulting map split the largely African American city of Jackson into five divisions, all without minority representation. Although lacking the abstract expressionist geometry of what we commonly think of as a gerrymandered district – the divisions were simple, rhomboid-esque shapes – Hinds County had all the political implications of one. 

Graphic via "The Promise and Perils of Computers in Redistricting," 2010, Duke Journal of Constitutional Law & Public Policy

The Hinds County districting algorithm was made in a time before computers, but it brings up the same complications inherent in automated redistricting. If we agree that districts that imitate oblong paint splatters are unjust, but simplistic shaped objects that divide a community into one without a voice to be unjust as well, then what exactly defines a boundary as being fair? America’s political geography of dense, urban Democratic centers surrounded by Republican-dominated rural areas makes defining an algorithm that doesn’t disenfranchise voters incredibly difficult.

But that is only the beginning of the computational complexity of automating our internal political borders. In a landmark 2010 paper in the Duke Journal of Constitutional Law & Public Policy, Micah Altman and Michael McDonald argue that "the problem of creating optimally compact, contiguous, equal-population districts is provably 'NP-hard.'" In other words, with only a small handful of variables the problem becomes incredibly complex very quickly, so complex that it is "probably impossible to create a computer program that solves these problems optimally and reliably except in very small or limited cases."

Creating "optimally compact" districts is, by itself, a complex quandary as there are an exponential number of ways that a district can be drawn to be compact. And those are just the basic variables. There are often a host of other concerns that are worked into region definition that complicate the situation: coincidence with other boundaries, easily identifiable regions, geographic monuments, defining an area by "communities of interest" or what is termed "vernacularly insular" – a complicated way of saying the designated region should actually be representative of a community that has historically lived there. 

Once these restrictions are decided on, then there is the matter of deciding between which mathematical model best approximates the optimum layout for, say, Oklahoma’s 14th district, whether it be a q-state Pott’s model or a weighted Voronoi diagram. Choosing an algorithm that defines the boundaries is, in itself, a political decision that can never be value-neutral. Feeding the result into a complex set of equations that the lay resident won’t be able to comprehend actually mires the problem even further.

Altman and McDonald also believe that the advancements in computers and GIS software being used to gerrymander districts are not corrupting the process. In a separate study, they found no "statistical correlation between computer use, computer capabilities, or use of electoral data, and gerrymandered districts."

There was of course a time when the computing power needed to run advanced districting software was a luxury item solely purchased by state governments, but now any reasonable desktop computer can do the same work using free, open-source programs like BARD or DistrictBuilder. No longer the realm of the few technocrats at the helm of obtuse, expensive software, the current movement toward "open redistricting" intends to make the process more of a public consensus. Although they are not automatically generating boundaries, these systems use heuristics – educated guesses to help solve a problem – as a guide for redrawing congressional boundaries. The one major success story of algorithmic redistricting in this way would be Mexico’s Federal Electoral Institute, which does use a simulated annealing method as a heuristic to define their districts. Those plans are then presented in a public forum where other interpretations can be presented as an alternative and then voted upon.

The transparency and participation aspect of open redistricting is key. Anybody can draw a district with or without expensive software, but it’s a matter of drawing fair districts where the topic becomes divisive. The Public Mapping Project has been running a series of student mapping competitions to show that, yes, students with little knowledge of mapping, geography, or politics can draw fairer districts than those created by representatives of historically gerrymandered states like Virginia. 

Having software that can compute complex metaheuristics certainly helps, but it is meaningless without a public process to help decide upon the results. Otherwise, any number of variables can be tossed in to skew the results one way or another. And the issue of gerrymandering has never really been about how to draw congressional lines, but instead who gets the final say in which version becomes law.

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