## Wednesday, May 04, 2011

### Using Math To Prevent Gerrymandering?

At first glance, it's an interesting proposal:
The degree of contrivance behind the design of a set of districts is directly related to the oddness of the shapes employed to reach the election-rigging objective. There is a precise mathematical way to measure such malformation. That is, if you take the square of the perimeter of any shape, and divide it by the shape’s area, you arrive at a number, which can be called its irregularity. For example the irregularity of any square, regardless of its size, equals 16 (because (4s)2/s2 = 16.) On the other hand, the irregularity of a rectangle whose long side is 10 times the length of its short side is 48.4 (because (22s)2/10s2 = 48.4.) The odder and more contrived the shape, the higher will be its irregularity.

Now congressional districts need to have equal population sizes, so the task of dividing a state fairly is more complicated than simply slicing it up into low-irregularity shapes. Still, there is a solution which can be objectively ascertained that does accomplish the goal of creating equal population districts with the minimum total irregularity. This can be found either by humans or computers.

I suggest it be done as follows. Let’s let the majority party in the state legislature take the first shot at proposing a redistricting plan. The sum of the irregularities of all the proposed districts can then be added up to create a score for the majority plan. The minority party can then be given 30 days to come up with an alternative plan. If they can come up with a design whose irregularity score is 1 percent lower than the majority plan, then the minority plan is adopted. If not, then the majority plan remains in place.

Creating districting boundaries in this way will not prevent the creation of safe districts for one party or another in all cases. But it will leave the matter to fair chance and geography, rather than the arbitrary actions of political cabals.

#### 1 comment:

Eowyn said...

Why don't they use the census results and mathematical algorithms that will divid each state into N regions, each with almost exactly the same number of people.

There's a fairly simple algorithm, where you pick N centroids first, then assign each household to the nearest centroid. If not balanced, you recalculate the center of each region and rerun.

Given today's computers, this is perfectly feasible, and is used in data mining on a regular basis.

Of course, the problem with this algorithm is that it's colourblind. And gender blind. And political party blind.