Shortest Borderline Redistricting Algorithm

[Brian Langstraat]

Shortest Borderline Redistricting Algorithm (SBRA) would be a deterministic district-drawing algorithm similar to Shortest Splitline Algorithm (SSA) and Shortest Splitarc Latitude/Longitude Algorithm (SSLLA) that uses predetermined voting district borders.

For comparison to the SSA, the following is a modified version of its description:

Advantages

The advantage of having our simple splitting algorithm draw the congressional districts is obvious. There is one and only one drawing possible given the number of districts wanted, the map of the state (including voting districts), and the distribution of people inside it.

The SBRA for drawing N congressional districts

Formal recursive formulation

Start with the boundary outline of the state.

Let N=A+B where A and B are as nearly equal whole numbers as possible. 

(For example, 7=4+3. More precisely, A = ⌈N/2⌉, B=⌊N/2⌋.)

Among all possible borderlines along voting district borders that split the state into two parts with population ratio A:B (within 1% of ideal), choose the shortest. (Notes: the Earth is approximately an ellipsoid. Any ties (length within 1 meter) would go to the borderline that results in the closest to ideal population ratio. "Length" means distance between the two furthest-apart endpoints on the borderline, that both lie within the district being split.)

We now have two hemi-states, each to contain a specified number (namely A and B) of districts. Handle them recursively via the same splitting procedure.

Further simple rules could be setup to deal with: bodies of water/islands, cities/counties, the Voting Rights Act, etc.

Congressional districts created using the SBRA would have simple geometric shapes like those created by the SSA with bumpy edges like BDistricting.

The SBRA may be able to avoid the strange issues caused by the Chesapeake Bay in Maryland for the SSA and BDistricting, since the minimizing borderlines would reduce the chances of crossing large bodies of water.