A Multistart Constructive Heuristic Algorithm for Political Districting

For better or worse, state legislators are responsible for redistricting their state every ten years when new census data becomes available. Historically, it has often been a hard fought battle between opposing parties. Sometimes district lines are so hotly contested that the Supreme Court is forced to intervene. Whether or not anyone believes there is any wrong doing amongst the legislators, there is some benefit in finding a districting method which avoids such political strife. We propose an algorithm based on an idea of expanding bubbles. Imagine entities within a state, one for each congressional district, which expand until they fill the state. The bubbles push each other and deform in such a way that they eventually have no more room to expand; their edges form the district boundaries to be adopted. In implementation, the so-called bubbles expand based on rules that maintain their bubble-like shape, keeping them compact and contiguous. Deformation is modeled by a bubble’s preference to grow in an empty space not taken by a competing area. This means two bubbles competing over the same area will deform into each other. To model bubbles pushing one another when they have no room to expand, a bubble might steal parts of a neighboring bubble, forcing the neighboring bubble to expand into empty space. And finally, each bubble in the simulation expands at the same rate. Of course, no actual state has a uniform population density. The rate of growth of each bubble is dependent upon the population it encompasses. Thus at the conclusion of the algorithm, the bubbles are equally populous, connected, and reasonably compact: the only characteristics that yield a universally fair districting scheme. Upon applying this algorithm to the state of New York, the results are found to be acceptable for this type of model. Although there were several poor solutions found, these are expected due to the probabilistic nature of the algorithm. Furthermore, it is believed that with ample computational power, even these lessthat-optimal solutions would converge to suitable districting schemes. There exists a strong possibility of implementing a more efficient bubble expansion algorithm. The current version uses a coarse discrete approximation to a continuous problem. Significant computational efficiency may be gained by formulating a discrete version. This opens the door for some very interesting future research.