Sunday, October 08, 2017

The redistricting method of the future

Maryland Redistricting Reform Commission
Office of Governor Larry Hogan

Honorable members of the Redistricting Reform Commission:

Maryland law says: "Each legislative district shall consist of adjoining territory, be compact in form, and of substantially equal population. Due regard shall be given to natural boundaries and the boundaries of political subdivisions." Census tracts average about 4000 people, but in Maryland some census tracts have 24000 people. There are currently 1394 census tracts for about 5.8 million people. A Senate district is currently sized at 123,000 people +/- 4.7%. There are about 30 tracts per Senate district.

These numbers are well suited for mathematical optimization. The general idea is to define the redistricting task as sets of constraints and one or more optimization goals that are precisely defined as equations. Some optimization methods require a single optimization equation. Combining multiple optimization goals that are represented by different units of measurement can be a complication. It is possible to utilize multiple optimization goals that are represented by a common measure, such as a percentage, to avoid this complication.

The more goals there are the greater the risk that different goals will conflict with each other. The tighter the constraints the more likely that there will be no feasible solution. Therefore, it is preferable for the number of different optimization goals to be low or be selected to be non-conflicting and to take precautions that ensure the constraints are realistic.

Contiguity is a constraint. A maximum count of district boundaries crossing significant political subdivisions and natural boundaries are additional constraints. The Redistricting Reform Commission is proposing a maximum +/- 1% population variance which could be implemented as another constraint. Maximum compactness can be the optimization goal, or compactness could be combined with minimum population variance as the optimization goal.

Viable optimization algorithms for redistricting are heuristics that obtain a good result quickly. This is because redistricting optimization is technically a very difficult problem to solve given the vast number of possible solutions. Different software on different computers with different optimization algorithms will produce different results. These different results can be ranked by the optimization goals equation. This presents an opportunity to implement redistricting as a contest. Competitors can be given instructions for how to submit redistricting map proposals. The earliest submitted redistricting map that generated the highest optimization score while meeting all constraints would be automatically adopted. As an incentive the winning proposal could receive a cash award.

Compactness can be measured by boundary shape. Or by the degree to which the district spreads from a central core, called "dispersion". Or by housing patterns, which is sometimes referred to as population compactness. District tendrils are less meaningful in sparsely populated areas but more meaningful where the population is densely packed. The ratio of the proposed district's perimeter and the perimeter of a circle with the same area size is an example of a boundary shape measure of compactness.

Members of the Redistricting Reform Commission should consult with the computer science and mathematics departments at universities and colleges, particular those that offer graduate degrees in Operations Research, for expert advice. Examples of automated computer redistricting, some with free source code, are available on the Internet (,,,, and Applicable algorithms include polygonal clustering, graph partitioning, simulated annealing, and tabu search, among others. Spatial contiguity can be formulated in a mixed integer programming framework, so mathematical programming methods may also be viable.

The district boundaries after each census could be very different from the prior boundaries, which can contribute to making elections more competitive. The result of relying on mathematical optimization for redistricting will be gerrymander free and fair by the "justice is blind" standard. There is no need for a redistricting committee. A voting rights committee composed of former judges could be responsible for splitting some Senate districts into two or three Delegate districts to try to ensure compliance with the Voting Rights Act of 1965.  

Currently the Delegate districts are three member by default but with 16 one member and 12 two member districts that are not publicly explained. The Governor's Redistricting Reform Commission is recommending one member Delegate districts by default with fewer exceptions. However, one member Delegate districts give each citizen fewer representatives assigned to different committees which weakens citizens' influence over the bills. The committee votes on bills are more important than the floor votes because bills that fail in committee almost always die and bills approved in committee usually also pass when they go to floor vote. The small size of single member Delegate districts risks rendering a +/- 1% population variance constraint along with the other constraints impossible. Also, one member Delegate districts undermines Maryland's ability to demonstrate compliance with the Voting Rights Act because occasionally merging Delegate districts is unlikely to increase minority representation. 

It may be better to retain the current three member Delegate district default and require that all exceptions be justified in writing as promoting increased minority representation in accordance with the Voting Rights Act. Alternatively, mathematical optimization could draw three Delegate districts in each Senate district but with somewhat different constraints and optimization goals then were utilized to draw the Senate districts. In particular, the optimization goal could be revised to prioritize meeting the requirements of the Voting Rights Act and the constraints could be loosened for those Senate districts that have a demographic profile which introduce Voting Rights Act compliance concerns. Dividing each Senate district into three Delegate districts could be a contest for finding the best redistricting map. This would create a two phase redistricting process, Senate districts first, Delegate districts second, that will increase the time needed to complete redistricting.

Federal redistricting standards are somewhat different from the state standards.  Also, Congressional districts effect the national election and thus are no longer only about the state of Maryland. If Maryland stops gerrymandering Congressional districts while Republican states continue to gerrymander then the next federal elections results will be more favorable for Republicans. It is more likely that a General Assembly redistricting reform bill will be enacted if it is not paired with Congressional redistricting. Therefore, it would be better for the Governor's office and lawmakers to place Congressional redistricting reform proposals into a separate bill, or postpone Congressional redistricting reform until after a multi-state reform collaboration effort that crosses the partisan divide is arranged. 

Mathematical optimization is the redistricting method of the future. Reliable enabling technology is available. Maryland has people with the skills needed to implement automated redistricting. I appeal to the Commission and state lawmakers to seriously consider mathematical optimization for redistricting.

Mathew Goldstein

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