Drawing Electoral Districts

Gerrymandering

One of the ways career politicians have developed to subvert elections and keep themselves in power is called gerrymandering. This is the technique of drawing the boundaries of electoral districts so as to favor their own reelection or the election of a politician from a particular political party. Blatant gerrymandering has been carried out for decades in plain view. The public is generally aware of it, but politicians don’t seem to be at all embarrassed about it and have thwarted all efforts to eliminate the practice — this in spite of the fact that 80% of voters favor its elimination. (See the “Career Politicians” page of this website.)

“Packing” and “cracking” colloquially describes the process. First, draw as few districts as possible to contain the maximum possible number of opposition voters (packing). Second, distribute the remaining opposition voters to keep them in the minority in as many districts as possible (cracking).

Legal specifications usually call for district to be “compact” and “contiguous.” Historically, gerrymandered districts have been the opposite of compact. The illustration shows Pennsylvania Congressional District 7 as it actually existed between 2011 and 2021. It was so obviously gerrymandered that it picked up the name, “Goofy Kicking Donald Duck.” More recently, digital computers have enabled politicians to gerrymander more efficiently and less obviously (achieve more compact shapes).

Misleading Notions

Of course, it is the politicians themselves that are the primary obstacle to eliminating gerrymandering, but several misleading notions have greatly aided them. These ideas have become stuck in many people’s brains and are extremely difficult to dislodge. They misdirect attention and cause never-ending heated debate about irrelevant issues.

Citizens’ Commissions It is a perennial proposal that an “unbiased” citizens’ commission be assigned the responsibility for defining electoral districts. No one with the intelligence to define electoral districts is going to be completely unbiased. So the selection of commission members is problematic. Shielding them from nefarious “influences” is difficult at best. Does it make sense to put together a new group of people every ten years and have them reinvent the redistricting wheel? There likely would be next to no transparency into how they went about doing their work. If their work is disputed, it ends up in the courts, with hard-to-predict and sometimes arbitrary results. Courts are not necessarily politically neutral. However, if we didn’t have any better solution, such a commission would probably be some small improvement over leaving the responsibility directly with the politicians.

Communities of Interest (CoI) Many redistricting guidelines discourage having district boundaries divide political entities, such as counties. Not dividing political entities stems from a desire to not divide so-called “communities of interest,” which are blithely presumed to coincide with political entities. There are two fundamental and fatal problems with the notion that communities of interest should be kept together: one is practical, and the other is principle based.

The fatal practical problem is that CoI is a very nebulous and hard-to-define concept. Different people will have radically different definitions. CoIs can be based on religious beliefs, political philosophies, single hot-button issues, and countless other criteria. CoIs as defined by different people can and will differ and overlap. Whose definition is to be adopted? CoIs can shift and change considerably from one election to the next, depending on the hottest issues of a particular election. Not dividing CoIs is a poorly defined and completely insoluble problem of impossible complexity. It’s an exercise in futility that obviously cannot be solved by mere mortals, whether they are state legislators or citizens on a commission.

The fatal problem of principle is that the only possible valid reason anyone would want to keep a CoI together in an electoral district is so that a representative who “truly represents their interests” can be reliably elected. The only way that can happen is if the members of that CoI can outvote a smaller number of those in their district who do not share their same interests. That is the very definition of gerrymandering, which presumably we are trying to prevent! Oops.

We have lived for decades with districts that slice and dice counties in all manner of arcane ways. We have suffered zero harm caused by the division of political entities. However, we have suffered harm, all of which was caused by contriving districts to keep communities of interest together, where the communities of interest are those who share the philosophy of a specific political party!

Electoral Districts Must Be Fairly Drawn This is a misstatement of the objective. The word “fair” should never be used in this context. It is highly subjective and means different things to different people. If the word is used, it is necessary to spell out in considerable detail the objective criteria to be used when judging fairness or unfairness. This is rarely done, so confusion reigns and progress becomes impossible without agreement.

The correct statement should be that electoral districts must be impartially drawn. “Impartially” has an objective definition. In this context, it means that districts must be drawn in such a way that does not confer any systematic advantage or disadvantage to any particular faction (or community of interest, if you prefer). All the muddled thinking surrounding redistricting has made it even easier for politicians to stay in the driver’s seat and keep right on gerrymandering.

The Precinct-Preserving Splitline Procedure (PPS)

Suppose it were possible to write down a clear and concise procedure to define electoral districts that is guaranteed to be completely impartial. Such a procedure could be followed by anyone, or even a computer, and the identical impartially drawn districts would be the result. And suppose that the same straightforward procedure could be used to quickly and impartially draw equal-population districts very accurately for any number of districts and for any state. The procedure could be enshrined in the Constitution, and there would be no need to reinvent the redistricting wheel every ten years. Redistricting could be done quickly, at a very low cost, and without all the strife. The process would be completely transparent, and anyone could verify that districts have been correctly drawn.

The good news is that such a procedure was written down in 2009 and is available for use at any time. It is called the precinct-preserving splitline (PPS) procedure. It has just five steps. It will never divide voting precincts and always produces equal-population districts that are maximally compact. Here is the PPS procedure:

In all cases in which a political entity (e.g., a state) is entitled to elect multiple representatives, the procedure defined here must be used to determine the electoral districts for such representatives. Voting precincts will never be divided. The geographic boundaries of political entities (states, counties, municipalities, and precincts) and the total populations for each voting precinct are the only data to be utilized. Note that party affiliation, voting history, race, gender, etc. may never be considered.

If the population of the political entity is p, and the number of districts to be drawn is n, the following (sometimes iterative) procedure is to be used.

  1. If n is 1, no subdivision is necessary, and this is a final district. If n > 1, then define two new numbers, i = n/2 rounded up and j = n/2 rounded down. (Note that i + j always equals n, and if n is even, i obviously will equal j.)
  2. Draw the shortest possible (great circle) line dividing the area into two sections so that one section has a population equal to p multiplied by i/n, while the other section has a population equal to p multiplied by j/n. If there is more than one equally short line, use the line closest to a north-south orientation, and if there is still a tie, use the westernmost line. For irregularly shaped entities, it is possible that a line could exit and then reenter the entity; the length of the line is defined as the total distance between the two most distant points of intersection that lie on the boundary of the area being subdivided.
  3. Make a list of just the voting precincts that have parts of their area on both sides of the great circle line just drawn in step 2. If 80% or more of any split precinct’s area lies on one side of the line, assign each such precinct entirely to that same side of the line and remove it from the list. Sort the remaining list in the order of the largest population precinct to the smallest population precinct.
  4. If there are any precincts on the list, assign the first (largest) entirely to the side of the line that needs the most people to hit its target population. Repeat this step until all precincts have been assigned.
  5. The division of the original large area into two sections has now been completely defined. For each of the resulting two sections separately, go back to step 1 using the section’s population for p and either i or j (whichever was associated with the section) as n.

Those not mathematically inclined will prefer to have a visual illustration of how the procedure works. The state of Pennsylvania will be utilized as an example. If Pennsylvania had just one representative, there would obviously be nothing to do, and the entire state would be the one required district.

This first map shows Pennsylvania with two districts. The procedure draws them simply by finding the shortest possible line that divides the state into two sections, each having half the population. Nothing could be simpler or more impartial. If that line splits any voting precincts, a simple rule determines on which side of the line each split precinct is to be placed so as to maintain its integrity. Those familiar with this state will quickly understand that the very heavy population density associated with Philadelphia in the southeastern corner of the state causes the splitline to occur (perhaps surprisingly far) toward the eastern end of Pennsylvania.

This second map (below) shows Pennsylvania with three districts. The procedure tells us to first draw the shortest possible line that divides the state into two sections, one having 1/3 of the population and the other having 2/3 of the population. Finally, the shortest possible line is drawn, which divides the larger section into two districts, each having 1/3 of the population. After each line is drawn, any voting precincts that would have been split are placed entirely on one side of the line or the other, as determined by the simple rule that is part of the PPS procedure.

The next map shows Pennsylvania with four districts. First, draw the shortest possible line that splits the state into two sections, each having half the population (the same line as drawn for the two-district case). Next, draw the shortest possible lines that split each of those sections into two districts, each having one-fourth of the population.

For any number of districts, just follow the procedure, and the required number of equal-population districts will be impartially drawn. Now that the basic operation of PPS should be clear, we jump to a map of Pennsylvania with the seventeen districts that it actually has. Notice that for seventeen districts, the first splitline now divides the state into two sections, one having 8/17 of the population and the other with 9/17 of the population. This is the first step in defining eight districts to the west of that line and nine districts on its east side.

Finally, just for pretty, here is a clean map of the seventeen districts without all the explanatory notations.

Drawing straight (geodesic or “great circle”) splitlines can achieve equal population districts extremely accurately. However, preserving the atomicity of voting precincts will inevitably introduce some errors in population equality. But even for the smallest districts (containing about 30 precincts), population errors will be less than 1% which should be entirely acceptable.

Acknowledgements

The basic splitline procedure was invented circa 2002 by Warren D. Smith. Basic splitline is ruthless and splits anything and everything in its path. Voting precincts are sliced and diced. At the lowest level, it provides rules for locating a split residence entirely on one side or the other of a splitline.

The PPS procedure was independently invented by Roy Minet circa 2009. PPS employs basically the same underlying splitline process but includes the precinct-preservation feature that renders it a practical solution.

The excellent map work was graciously contributed by geographic information systems professional Stephen Kruzik. His contribution is greatly appreciated.

More Information

The Precinct-Preserving Splitline (PPS) method of drawing electoral districts was advocated and explained to the Pennsylvania House State Government Committee during a hearing held in October of 2021. Here is a transcript of that testimony: House State Government Committee PPS Testimony

This book cover gerrymandering and all key election problems in considerable depth: Elections Are Broken — How to Fix Them