Measuring Ohio’s Gerrymandering Spike – A Proposal For Fair Election Maps

I’ve created a simple tool to measure Ohio’s gerrymandering, which is the mapmaking cheat that gives a political party more election wins than they deserve. Ohio’s maps are so bad they were ruled unconstitutional by a federal court. The timeline above shows the full 200 year history of Ohio’s Congressional maps using a heat map of gerrymandering, which clearly shows a spike in unfair districts since the 1970’s, when the invention of computers enabled cheaters to maximize their partisan mapmaking. This data also enables us to propose an objective standard of what we should expect from mapmakers who will be drawing our new maps later this year in 2021.

A Heat Map of Unfair Districts

The image below is Ohio’s current Congressional district map analyzed by my tool, colored as a heat map with more unfairly gerrymandered districts having a darker shade of red. The scale I’ve developed is shown in the legend, where a fairly compact district is shown in white, and the most unfairly contorted districts are the darkest. Notice how the darkest districts have very strange shapes missing large chunks out of them.

Here is the map from 1969 using the same heat scale. Notice how much lighter the whole state is and how much more compact the districts were:

There was likely some gerrymandering in this map too, but at least it’s not quite as bad as it is today. As you can see in the timeline at the top of the article, most of the district heat maps before 1970 were about as light as this one, but after that they’ve only gotten more gerrymandered.

Compact Districts Create More Fair Elections and Better Representation

Ohio’s Constitution now requires that “Every congressional district shall be compact.” When districts are compact, communities with shared local interests are held together and elected officials can better represent their priorities. When districts are bizarre, squirrelly shapes, it’s usually because mapmakers are trying to cheat at elections by (a) separating people to drown out their voting power or (b) singling out a certain type of voter and connecting them with people who don’t live anywhere near them. Either way, the goal of gerrymandering is to take representation away from people.

A square is perfectly compact and earns a 100% rating, while a star is more abnormally shaped at around 73% compact. The original gerrymander district was only about 44% compact:

When districts are gerrymandered, they tend to be much less compact, and that’s exactly what happened to Ohio over the years. Let’s look at the data more closely to better understand the problem.

Plummeting District Compactness

For 160 years Ohio’s congressional districts were consistently more than 81% compact on average. From the very first district maps in 1813 until 1973, our districts were more reasonably shaped. But since then, average district compactness has steadily dropped to 75% in 1993, 70% in 2003, and plummeting down to 62% with our current unconstitutionally gerrymandered maps drawn in 2011.

Notice that median compactness was also above 80% for even longer, and consistently above average for nearly 200 years until recently when the median saw a sharp decline, reaching under 57% in today’s maps.

(Note that districts were not required to be equally populated until 1964, but that doesn’t explain the steady drop since 1973.)

Bare Minimum Expectations

At a bare minimum, it is reasonable to expect districts to be at least 50% compact. Below that a district is objectively more indented than it is compact.

Throughout our State’s entire history until 1953, there had never been a district less than 50% compact. For the next 40 years, there was only at most 1 district below that threshold, but in 1993 that number jumped to 3. Today we have 4 districts below 50%, 3 of which are in the low 40’s. That’s a quarter of our districts which are objectively not compact.

It gets worse if we bump our bare minimum to 56%. Prior to 1969, we only had at most 1 district go below that, but it has only become more common since then. Today there are 8 districts that are less than 56% compact, more than doubling the previous record. In other words, half of our current districts are below a threshold that had never been crossed by more than 5% of any map’s districts in the first 156 years of our Congressional districts’ history.

Here are all 16 of today’s districts sorted by compactness, with the worst districts at the bottom. This data is used for the map at the top of the article and is colored coded using the same heat map scale:

District 11 (from Cleveland to Akron) is the worst Congressional district in Ohio at only 40%:

Establishing Standards of Compactness

Now that we’ve quantified the long historical precedent of reasonably compact districts and the clear outlier exemplified by our current unconstitutional map, we should be able to establish a reasonable and fair standard of compactness somewhere in between.

Here is a first draft, which we’ll test and improve further below:

1. Average and median compactness should be at least 75%, something we’ve nearly accomplished in all but the last 2 decades. Preferably above 80%.
2. No district should be under 40% compact, which has almost always been true. Preferably no lower than 50%.
3. There should be no more than 3 districts under 55% compact, which is true for all but our current map. Preferably no more than 1-2.

To test these draft standards, I checked them against hypothetical Ohio gerrymandered maps created by FiveThirtyEight.com, one favoring Republicans and another favoring Democrats, each giving more reliable seats to their party than they currently have. Surprisingly, both had average compactness at 75-76% and medians at 78-83%, although both had fairly low minimums of 42-43% with 2-3 districts under 55%. Both barely met all the draft standards, but failed at least 2 of the preferred standards, suggesting that we’ll need to raise the bar higher.

FiveThirtyEight also included a competitive map, which created fewer reliable districts for both Democrats and Republicans while creating more competitive elections. It had high average and median values of 86% and 88%, but had 1 low quality district at 47%: the 11th District which they left about as gerrymandered as it is today. This map is an improvement, but we can do even better…

A Nice Compact Map

Now let’s look at FiveThirtyEight’s compact map:

When I analyzed this map, I was blown away by the results. It achieved a fantastic average and median of 93% and 95%, with an excellent minimum of 78%, far surpassing all 3 of our first draft standards. Note that this map is fairly realistic since it follows county lines, meets the population requirements, makes discrete districts for our cities while giving a realistic Republican advantage in rural areas, all while still creating lots of competitive districts. They clarify that it may need to be tweaked to meet all State and Federal laws, but this map shows incredible promise for very high standards of compactness to produce fair maps.

Higher Standards: The Final Proposal

Given these findings in addition to the historical precedence, I propose these more robust standards for immediate use in Ohio’s upcoming redistricting process:

1. District average and median shall be at least 85% compact.
2. No district shall be less than 60% compact.

Both of these standards have been met for most of our State’s history and we can reasonably expect to be able to reach them again. In 2022, we may lose a Congressional seat, leaving us with only 15 districts, which has never before happened in our State’s history (usually we had 19-24 districts). Other than our current map, the closest would be in 1823 which had 14 districts. That map had an average compactness of 90% and a minimum of 78%, well exceeding these proposed standards and achieving a wonderfully compact map:

The State of Ohio itself is actually quite compact at 97% compact. With only minimal cavities from Lake Erie and the Ohio River, the state’s shape does not hinder our ability to make good districts like it might in Maryland for example. The Ohio Constitution’s new rules specify that counties must generally be kept together and used as building blocks for districts, and Ohio’s 88 counties have an average compactness of 97% and minimum of 88% (the heat map would be completely white):

Therefore expecting an 85% average from our Congressional districts is really not too much to ask. Let’s make these standards a reality in 2021 to improve our democracy and enable better representation for Ohioans!

How The Tool Calculates Compactness

To measure compactness, I implemented the technique described by mathematicians Jonathan Hodge, Emily Marshall, Geoff Patterson, each from different US universities, in their 2010 paper Gerrymandering and Convexity, which was published in the College Mathematics Journal and won the 2011 George Pólya Award. “Convexity” is the technical term for what I’ve referred to as compactness.

Here’s how it works in a nutshell: pick two random points inside a district, draw a line between them and check if that line exits the district boundary or not. Repeat that process 100,000 times per district. Now divide the number of escaping lines by the total number of lines, and you’ve got your convexity coefficient, or what I’ve called the compactness percentage. In other words, it’s the odds that traveling in a straight line between two random locations within a district would require leaving the district.

There’s one small tweak to that: if any line exits the State boundary, then it’s not fair to count that against the district, so I don’t count that line and instead just pick a new one.

Below is how that measuring process looks when it’s visualized by my tool, which uses HTML Canvas and JavaScript. Contained lines are black and exiting lines are red. The State is completely covered by 1.6 million lines, which takes about 3 minutes for my computer to generate:

The authors of this technique applied it to all 50 states in 2010 and found that Ohio had the 15th worst rating, and that was before our most recent map which is even more gerrymandered. They calculated a statistical “95% confidence that our approximations have an error of less than 0.01”, although I used 10 times as many lines as they did.

Technical Notes and Other Considerations

The constitutional compactness requirement exists for the September and October deadlines, but if an impasse pushes into November, our constitution lowers the hurdle to “The general assembly shall attempt to draw districts that are compact.” Even then, the constitutional duty to try must be fulfilled by either delivering compact districts or else providing a reasonable explanation for why compactness was not achieved. The absence of both may be evidence of neglect of this duty or even intentional gerrymandering, which could be brought before the Ohio Supreme Court.

Ohio’s historical at-large districts throughout the years were excluded by the tool since they don’t represent geographic subdivisions. From our state’s creation in 1803 to 1813, Ohio had no subdivided districts and the State was represented in the House by a single Congressman, Jeremiah Morrow.

Our current official district shape file extends out into Lake Erie, which can artificially raise compactness ratings for northern districts. For all reports I restrict districts to land boundaries, which does include some islands on the Lake.

The State’s lowest rating was not as strong an indicator of overall gerrymandering trends compared to the number of low compactness districts. The current minimum is 40%, but 1987’s District 19, which wrapped around Cleveland, was the lowest in Ohio history, at just 25% compact.

There is an argument that compactness can be ignored in favor of improving the efficiency gap, but I disagree. That approach further entrenches the two party system at the expense of third party candidates, and I believe we would benefit from more diverse candidates, not less. That article also argues that bizarre districts are OK if the intentions are good, giving the example that grouping Hispanics from non-contiguous neighborhoods is a good thing. However, it’s problematic to assume racial groups or other demographics are expected to share the same policy priorities or candidate preferences, and to use that as justification for making non-compact districts. That could actually increase racism rather than alleviate it. In other words, we should be striving to make less racially motivated districts, not doubling down on them. Furthermore, we could get stuck in subjective arguments over intentions; whether a district is a good gerrymander or a bad gerrymander. In the long term, we’re better off removing intention in favor of more objective standards like geographic adjacency. Of course metrics like efficiency gap or demographic makeup can further refine our mitigation of partisan mapmaking, but compactness must come first if we still claim we’re making a “map of contiguous districts”. Further critiques can be found here.

There are other techniques to quantify compactness, such as Polsby-Popper or Convex Hull, which involve circling or enclosing the district. The advantage of the convexity coefficient method is that it can catch a “coiled snake” type district, accounts for state boundaries, is relatively easy to calculate, and importantly, is intuitive and easy to explain to voter and legislators. It does not account for an elongated rectangle, but that could be considered with a simple Length-Width ratio. I would not recommend assigning a relative weight to convexity and elongation, since that would likely be arbitrary, but rather add a separate elongation requirement based on its own analysis and historical precedence. Note that other techniques are all likely to show a similar declining trend in Ohio overall, albeit different relative values.

Compactness is not the only measure of gerrymandering, as mapmakers can still find ways to favor one party using only squares. However, without squiggly shapes it’s much harder to do, so high compactness mitigates the power of cracking and packing techniques. Of course other criteria besides compactness can and should also be used to ensure districts are even more fair, such as the boundaries of cities or other communities of shared interests. Nonetheless, I consider compactness the most objective and important aspect of fair mapmaking and this technique is a suitable yard stick to quantify it, which can help us keep constituencies together and create more confidence in our representative democracy.

A Call To Action

As of 2021, Ohio has 12 Republicans and 4 Democrats in the US House of Representatives, even though Ohioans identify as 42% Republican and 40% Democrat. Representatives are up for election every 2 years and in 2022 they’ll be running in new districts drawn under the new rules. I’ll be very interested to see if our new maps result in more compact districts and more proportional representation in next year’s elections.

I strongly expect to see our new maps exceed 85% average and 60% minimum compactness, and highly encourage maps well exceeding these limits. I ask that our State Legislators create highly compact district maps as required by the Ohio Constitution, and to publicly release digital shape files for any proposals under consideration, well in advance of their adoption, so that there’s plenty of time for public feedback. I hope you’ll join me in these demands. Please send this page to your State Senator and State Representative and ask them to ensure we get highly compact and fair districts.

Redistricting Underway

11/10/21 – A Joint Committee on Redistricting is considering congressional map proposals. House Democrats’ proposal nearly meets these proposal standards with a 83% average, 89% median, and a 60% minimum! It’s just 2 points shy of our standard for the average.

If adopted, this map would be the most compact Ohio map since 1963. However, the majority party is pursuing other proposals, and no other legislative sponsored map meets our standards. The unofficial Ohio Citizens Redistricting Commission and Fair Districts Ohio competition winners all exceeded our standards. Read our full report on 2021 Congressional district map proposals.

Resources

The second part of my series on gerrymandering, regarding State Legislative districts, can be found here: Ohio’s Unfair Maps – Fixing State Legislative Gerrymandering

Historical map files were produced by Jeffrey B. Lewis at UCLA and can be found here. This repository was incredibly helpful and I am very grateful for the work he and his team did to make this data available to the public.

Find your Congressional district and who represents you in Congress

Ballotpedia: Redistricting in Ohio after the 2020 census

Districtr: Draw your own district map

Wikipedia: Ohio’s congressional districts

League of Women Voters: Ohio’s Gerrymandering Problem: Why Haven’t We Fixed This Yet?

Cleveland.com: An Ohio congressional map that makes sense – un-gerrymandered