# Discussion

The discussion of our results can be broken down into two primary areas, first the recursive method used, and second the resulting districts.

By definition of the recursive method the first districts drawn will be able to roam freely across the state adding the tracts that best suit their value function since comparatively few of the tracts are already placed into districts.  The later tracts will have to add tracts with low score values since they are geographically bounded and won’t reach the target population.  In our data districts one through six were able to be computed with minimal loss and interference but districts seven and eight suffered the most from this.  As a result these districts have some of the highest standard deviations across all three of our variables.

Using the simple compactness condition actually created surprisingly good results.  They pass the eye test since they are in fact far more compact than Maryland’s existing districts.  Due to the clumping nature inherent in this selection method many of the numerical problems present in our method did not emerge here significantly.  We were able to set our slackness term to 1/3 of what we needed in order to get a result for the value function.  As a result the correction phase played a relatively minor role here.

Adding our value function instead of emphasizing compactness changes a lot of our results.  At first glance these districts are a lot less logically shaped.  Our complex value function the recursive approach led to a lot of districts ‘running’, and ‘circling’.  A district running is when the algorithm forms a bridge between two areas with similar demographic information.  Circling behavior is when a district primarily based in rural or suburban areas does not want to add urban tracts to itself as the value functions for this tract are very low.

Encirclement in District 5                                                Running in District 7

Additionally using the recursive method meant that we had to choose the starting tract for each district while this was done essentially at random from the pool of remaining tracts it inevitably lead to an increase in subjectivity of our results.  Also our value function struggled when all adjacent districts had roughly the same score.  This lead to districts becoming entangled in illogical ways, an example of this is the entanglement of districts three and four.

Interestingly the orange district was drawn before the blue one but the values for all of these tracts are similar so the marginal differences lead to a non-optimal shape.  Overall while the recursive approach did lead to some odd behavior it still generated a workable outcome that we believe are still superior to Maryland’s current districts.

We are happy that our value function lead to decreases in the standard deviation of age even at the cost of small increase in the standard deviation of family proportion and African-American population proportion.  Even though not all of the sigmas decreased, we still believe we constructed a value function that accurately reflects our defined communities of interest.  In our test cases, the ordering of the districts was subjective. There are no clear definitions of communities of interest so we had the freedom to define them ourselves and adjust our function accordingly. Reducing the sigmas of all three isn’t as important as reducing the sigma of age, as defined by our function; 17 is much larger than 5 and 1. This explains why only one of the sigmas decreased.

The resulting districts matched logical expectation in most places.  Furthermore, many of our districts follow well defined communities that should have their own representative.  For example, Appalachian west Maryland is entirely in District 5, the tech savvy I-270 corridor to the northwest of DC makes up almost all of District 2, and the agrarian/waterman communities of the eastern shore are contained in District 1.

In other places our method fails; District 8 is terrible and it exists as an artifact of the recursive method.  It is possible that our value function fails in creating districts that reflect the true communities of Maryland.  In order to improve our value function, we could take input from the public.  Community members can go to their officials and assist them with defining communities of interest.  We would adjust our algorithm to combine the census tracts that are in these predefined communities into one.  Nonetheless, we still believe our value function created workable districts in its current form.

It is possible that the solution to the redistricting problem is to turn away from it completely.  Now that the world is so connected, geographical location isn’t as important anymore.  It is possible that the need for contiguous voting districts is outdated.  These regulations were created in the 18th century when most Americans were farmers.

An alternative solution is popular vote.  If each state were to create one voting district, there wouldn’t have to be a winner-takes-all voting system.  This would work perfectly under the assumption that Democratic and Republican candidates were interchangeable with each other.  Unfortunately, this is not true.  There are issues with popular vote as well.  If states implemented a ranked voting system, states could solve the problem with non-interchangeable candidates.  This starts to get ugly in bigger states like California.  Voters don’t have the time to familiarize themselves with 53 candidates that they would vote for.  Similarly, candidates don’t have the time or resources to campaign to the entire state of California.  It is currently much easier for voters to focus on only one election.  Popular vote may not be any easier to implement than winner-take-all elections in voting districts.