After having an hour-long conversation with a professor in the Computer Science department about gerrymandering, I decided to independently research the topic in pursuit of an answer to one of our most baffling questions:

“If the political capital exists to follow through with true redistricting procedural reform; then which solution(s) should we, as voters who would prefer our votes not be systematically diluted, promote?”

The Heartland explores where the problem lies mathematically:

By the conjecture of the author, Daniel Polsby, the current redistricting requirements of contiguity and equinumerosity are not sufficient for effectively warding off gerrymandering. One example of a heavily and obviously gerrymandered district that satisfies contiguity and equinumerosity is Illinois’ 17^thcongressional district – the infamous ‘rabbit on a skateboard’.

Polsby identifies a new, third criterion that would effectively eliminate gerrymandering – compactness. One of many alternative definitions of compactness (and my favorite) is the area of the district contained within its boundaries divided by the area of a perfect circle with the same parameter.

The justification for using a perfect circle as the divisor is that a perfect circle is the most efficient two-dimensional geometry in terms of capturing area per unit perimeter. The circle ‘normalizes’ the results so that the ratio always comes out to be between zero and one and is always a rough measurement of the subjective compactness of the district being measured.

This WordPress activity suggests that you use the centrality of population centers as a potential metric. While this metric is a little bit more difficult (though not impossible) to mathematically define, I believe that optimizing it is counterproductive; consider the modern case in which Democratic voters tend to cluster in urban areas – optimizing the centrality of population centers would cluster Democratic voters in districts that vote 70-80% Democratic (“stacking”).

This stacking would dilute Democratic votes in other districts, gaining Republicans many congressional seats in a state in which they may be equally popular with the Democratic Party.

In recognition of the completeness of the WordPress article, it does reference ‘compactness’ as a potential measurement to optimize in developing fair congressional districts that are in accord with democratic principles.

While optimizing compactness is an attractive option, the method that we use to optimize compactness is not as well-defined. It’s very easy to argue by example that it’s a desirable property to have electoral maps that are very ‘compact’, but it’s hard to explain how to get there. This ambiguity also leaves room for less-effective gerrymandering (gerrymandering within enhanced constraints).

My favorite solution solves for this non-determinism by providing a deterministic algorithm with a variable termination point (perhaps number of districts in accordance with a constitutionally-defined representation ratio?). You can find it here:

As a Texas resident, I feel comfortable in hypothesizing that this solution, the “Splitline Algorithm”, would make Texas a very different state than it is today.

By:  Ryan Roberts

(Photo by faul under a Creative Commons License)