It's Time to End Gerrymandering I: Disproportionate Outcomes

Representative forms of government are supposed to operate on a simple principle: citizens choose which politicians makes up their government. Gerrymandering, the term used to describe deliberate manipulation of the electoral process by drawing non competitive districts for congressional and state assembly races, flips this on its head. The government is then allowed to choose which citizens make up their constituency. Politicians do this to eliminate competition in elections, removing the primary way for citizens to hold their representatives accountable. This is also done by political parties to boost their share of seats in congress and state assemblies relative to their share of votes. Over time, gerrymandering can even lead to single party rule. Once elections stop being competitive, assuming citizens do not disengage from the political process completely, they may begin to see that joining the ruling party is a better strategy to getting their voice heard than attempting to oppose them. 

Gerrymandering is tantamount to voter fraud in terms of it's effect on elections, and it is possible to quantify how many citizens have been disenfranchised by gerrymandering around the country. So how is it legal, or even possible for that matter? The simple answer is that in most states the process of drawing district boundaries is completely or partially controlled by state legislatures. District maps may be drawn to confer a partisan advantage, to protect incumbents, and have even been drawn to shut racial minorities out of the political process. The fact that the government has the power to shield itself from accountability by rigging non-competitive elections is completely preposterous. At a bare minimum, this power should be taken away by turning over the redistricting process to independent, non partisan commissions. Any partisan political entity should be removed entirely from the process. Further, such a commission must be completely transparent, and should disclose all data that was used in redistricting process and for what purpose it was used.

If this intro is enough to convince you, then here is a form letter that you can send to your state representatives urging them to pass legislation to turn over the redistricting process to an independent commission. Otherwise, keep reading and we'll go into detail on how exactly gerrymandering is done, and how it can be detected and fought in a series of posts. If you have never heard of gerrymandering before, this series of posts is probably not the best place to start. This article does a great job of covering the basics, so we won't try to rehash it. This first post will be about disproportionate outcomes, where a party wins congressional seats out of proportion to it's level of voter support. While it might not seem obvious, a disproportionate result does not necessarily give us evidence of gerrymandering, because electoral systems with single winner districts rarely produce proportional outcomes. They simply are not designed to, in contrast to a proportional representation voting method.

The following two posts will be on statistical tests that can be performed to detect irregularities in voting results that may indicate partisan manipulation. We'll even introduce our own tests for detecting partisan and bipartisan gerrymandering. Following that, there will be two more posts on geographical methods for examining gerrymandering. These methods make for great visuals, but they are not always reliable for detecting gerrymandering. A district may have a strange shape for legitimate reasons, and a state with neatly shaped districts may still be gerrymandered for partisan advantage. This is why we've chosen to put the statistical tests first. Ultimately, someone looking to gerrymander a state is trying to eliminate electoral competition and create safe win districts, and this is what the statistical tests try to uncover. Creating safe wins for a party may require distorted districts, or it may not. Since unusual safe wins are what we are trying to find, the shape of the district is secondary.

But first, we'll discuss disproportionate outcomes, which sheds lights on one of the fundamental flaws of our system for electing congressional delegations and state assemblies regardless of the role of gerrymandering. The data used in this post comes from Daily Kos Elections, who have compiled district level results for the 2008, 2012, and 2016 presidential elections. We are therefore not using results from actual congressional elections. The presidential election data is very useful for getting a bird's eye view of gerrymandering since it is generally correlated with congressional elections as partisan voters tend to be loyal. This also gives us information for every district in the country in the same election in three different years, which is very useful for comparison purposes. 

Tyranny of the Majority

The first thing we can look at to try to uncover gerrymandering is to look at whether or not a party won roughly the same proportion of districts and votes in a state. Below is a map of this difference in the Democrats share of districts won and statewide vote share for each state averaged over the past three elections. Throughout these posts, we will sometimes refer to the share of districts won by a party in a state simply as it's seat share. Since these are presidential results gathered at the congressional district level, they do not represent actual seats in congress, this is just some short hand that we're using. Negative values indicate that democrats won more districts than their share of votes, and positive values indicate that republicans won more districts than their share of votes. The difference in statewide seat and vote share is averaged over the three elections which helps highlight states which are consistently disproportionate in one direction.

Color represents the difference in vote share and seat share averaged over the 2008, 2012, and 2016 elections

Color represents the difference in vote share and seat share averaged over the 2008, 2012, and 2016 elections

Nearly every state shows some degree of partisan advantage in one direction or the other, and many states are significantly out of proportion. We can take a closer look at proportionality with a scatter plot of the Democratic seat share vs vote share for all states in all three elections. The blue line represents a proportional outcome, results below the blue line are disproportionate in favor of republicans, and above the line disproportionate in favor of democrats.

Proportional results are extremely rare, and highly disproportionate results are the norm. So is that it? Can we declare that the entire country is gerrymandered beyond recognition? Not quite yet, since with single winner districts proportional results are rare even without partisan manipulation. This type of system is referred to as majoritarian representation, and often results in an S-shaped plot of seats vs votes. This is shown below, note that the S shaped curve is just a qualitative visualization of how fair majoritarian outcomes may differ from proportional representation and is not meant to test for gerrymandering.

Majoritarian representation gives disproportionate voice to those already in the majority, so we know that this is playing some kind of role in the disproportionate results that we see here. We will have to distinguish legitimate disproportionate outcomes from the effects of partisan gerrymandering. In the next two posts, we'll discuss statistical tests which detect irregularities in the voting results and do not rely on deviations from proportional or majoritarian results. 

It is interesting that our system for electing congressional delegations and state assemblies would be this way, given that we know the founders were quite concerned with what they called the tyranny of the majority. Majoritarian representation actually increases the ability of a majority to steamroll those in the minority by tending to give the majority disproportionate power. However, the founders probably did not know this since the field of formal study of voting systems was just in its infancy at the time of the founding of the United States. Marquis de Condorcet was a contemporary of founders and had set forth some early results in what would later become the modern field of social choice theory in the 1950s, which deals with how to aggregate preferences of individuals through voting systems among other things. The particular form S-shaped majoritarian representation curve was published in 1950, although in that article the authors mention that a pattern of non proportional results was observed as early as 1909. The purpose of this little historical diversion is to point out the fact that the founders had a lot of good ideas, but a lot of their ideas don't hold up to modern scrutiny and don't seem to even align with their own intentions. Anyhow, you may have noticed that there were some states that won a majority of seats with a minority of votes. Let's take a closer look.

The Tyranny of the Minority

There were a few instances where Republicans won a majority of seats with a minority of votes. These inverted outcomes are highlighted in red below, and each instance is recorded in the following table.

State Elections Where a Majority of Districts were Won by the Losing party (Difference in Democrat Seats Share and Vote Share)
Wisconsin 2012 (-15.89%)
Pennsylvania 2012 (-24.83%)
Michigan 2012 (-19.09%)
Florida 2012 (-5.99%)
Minnesota 2016 (-13.31%)
North Carolina 2008 (-27.09%)
Virginia 2008 (-16.82%), 2012 (-15.21%), 2016 (-7.09%)
Ohio 2008 (-27.22%), 2012 (-25.98%)
Indiana 2008 (-17.19%)

Here again it may seem like this is proof of gerrymandering, but it's not enough on it's own because single winner elections can lead to these outcomes by chance. Republicans won a majority of districts while losing the statewide vote in Florida, Michigan, and Wisconsin in 2012, but over all three elections these three stated only showed a minor disproportionate advantage to Republicans. Minnesota favored Democrats on average in terms of disproportionate outcomes over all three elections, but had an inverted result in 2016. On the other hand states like North Carolina, Virginia, Ohio, and Indiana showed consistently large favor to Republicans. The average difference in democratic seat share to vote share for states with at least one inverted outcome is shown below.

Color represents the difference in vote share and seat share for states with at least one inverted outcome, averaged over the 2008, 2012, and 2016 elections

Color represents the difference in vote share and seat share for states with at least one inverted outcome, averaged over the 2008, 2012, and 2016 elections

Since inverted outcomes can happen by chance, spotting one is not good enough to declare that a state has been gerrymandered. Just like disproportionate outcomes in general, these seem like results that intuitively should not happen, but they can happen in our voting system by chance, and in certain cases it is a proportional outcome that might be unexpected.

What Next?

Since disproportionate representation is inherent to our voting system, a single disproportionate result can't be used on it's own as a way to detect gerrymandering. In the recent ruling of Whitford v Gil, the Wisconsin state legislative districts were struck down due to partisan gerrymandering using multi election analysis of disproportionate outcomes. The expert witness for the plaintiff's showed that the disproportionate outcomes were unusually large based on an analysis of historical election results, and consistently favored republicans over several elections. Resorting to multi election analysis is undesirable however, since citizens may be disenfranchised in gerrymandered districts for years before sufficient proof is available to fight back.

In the next post in this series, we'll discuss statistical tests that can detect gerrymandering in a single election year, but even these are not perfect. Our voting system leads to unusual results to begin with and is vulnerable to exploitation by gerrymandering, so the best way to fight gerrymandering is to prevent it from happening in the first place. State governments should not have the power to draw districts, this job must be left to an independent, nonpartisan, and transparent commission. For such a commission to truly be effective in preventing gerrymandering, I think it must at a minimum have the following characteristics

1. It must have the full legal authority to draw the legislative districts without requiring input or approval from the state legislature

2. It must be charged with drawing districts that are competitive, that do not confer partisan advantage, that do not disproportionate empower or disempower any racial or ethnic group, and that do not divide any communities of interest

3. It must publish the source code of any software used in the redistricting process, with no exceptions for proprietary software of third party consulting firms, and explain in detail how the software was used to accomplish the goals set forth in point 2.

4. It must publish all data used in the redistricting process, and explain how those data were used to accomplish the goals set forth in point 2.

Here is a letter that you can send to your state representatives urging them to turn over the redistricting process to a commission with those four characteristics. You can check whether or not your state has a redistricting commission and what authority the commission has here. Given the enormous harm that gerrymandering causes, establishing independent commissions for redistricting is an urgent matter. But suppose that every state adopts these, what then? We will still have a voting systems where disproportionate outcomes favoring those already in the majority are normal, and minority rule can also happen by chance. There are other ways to elect congressional delegations and state assemblies, which are designed to result in proportional outcomes. We'll try to give these more attention in future posts, but one example is called open ticket voting. In this method there are multiple winners in each congressional district, but each state would then have fewer districts to keep the total size of their congressional delegation the same. Parties run multiple candidates and any candidate who passes a certain threshold is guaranteed to win. The remaining open seats after electing the threshold winners are allocated in proportion to the vote share by party. Systems like this are more difficult to gerrymander, and are inherently more competitive, making drawing the multiple winner districts meeting the criteria in point 2 an easier job. First thing is first though, contact your representatives and demand that they turn over the redistricting process to an independent commission. The 2020 census will be here sooner than you think, and after that state legislatures around the country will be drawing districts to block your ability to hold your government accountable. 


All of the source code used for this post can be found on GitHub.