Redistricting Rules (and) Republicans

Control of Redistricting Process
by Number of Congressional Seats
"Other" includes states with only 1 congressional seat, independent redistricting commissions, etc. 

Introduction (10-15 Min Read)

Redistricting is as interesting as its import, bringing up fundamental issues in political science, economics, statistics, and social contract theory, as well as illuminating imperfections in the US Constitution. In fact, the phrase 'gerrymandering', referring to the negative process of politicians abusing redistricting laws, arose almost as soon as our Constitution was ratified. 

While we've had an intuitive sense of when and how politicians have exploited redistricting for at least two centuries, its only been in the past couple of decades that we've had the precise mathematical tools and computer resources to detect gerrymandering in a rigorous and statistical fashion. The implications are nothing short of a computational rewrite of the Constitution.

Republicans Rule Redistricting
After strong wins in the 2010 midterms, Republicans had "complete control" of 21 states' redistricting processes, while Democrats only had comparable control for 5 states. This led to GOP power of 210 congressional seats' redistricting, compared to a paltry 44 seats for the Democrats. You can see the magnitude by comparing the difference between the percentage of seats allocated with the percentage of votes per party, what might be called the proportionality gap. On average in 2016, a 1% increase in vote share led to a 2% increase in the number of seats for a given party.

This is calculated as the percentage of seats minus percentage of votes for Democrats in 2010 by state. This is influenced by many states where no Republicans or Democrats win, i.e. the aggregate percentage difference does not correspond to aggregate seat differences. Nonetheless, it is clear Republicans have significantly more states where they benefit from our current system. Data collected from ProPublica.

Undoubtedly, changing districts to benefit incumbents and partisans, the primary way politicians pick voters, gave Republicans an edge in the 2018 election. According to one estimate, partisan gerrymandering could have cost Democrats 10-15 seats or more, probably preventing an otherwise blue bloodbath. As one of the more egregious, and unconstitutional, examples, North Carolina voted 49.8% for Trump vs 46.2% for Clinton, yet Republicans control 10 of 13 congressional seats!

North Carolina Congressional Districts

Redistricting Rules Republicans (and Democrats) 

But insofar as the rules put in place for redistricting are so easy to game, can we really be surprised politicians leverage them in their favor? In most states, redrawing congressional districts is a legislative process that occurs every 10 years. If one party has majority control of their state's government, then it is fairly easy to pass laws to the benefit of that party; in this case, biased redistricting laws. Call it incumbency insurance.

Political Incentives

In fact, it would be foolish for self-interested politicians to ignore these short term incentives while allowing their opposing party to take advantage of them. This is why in 1980 the Republicans sounded like today's Democrats, complaining about the unfairness of the redistricting process. Historically, Democrats got the upper hand in redistricting procedures (see the chart below), although this has started to change due to geographical clustering of parties.

Brookings

Bonus for the Losers
According to one paper that studies the dynamics of geographical clustering and who benefits in a winner-takes-all system,

"Republicans benefit from the loser’s bonus in most of the large states of the Northeast and West Coast, while the Democrats benefit elsewhere. On balance, the loser’s bonus is beneficial to the Republicans, and the size of U.S. Congressional districts relative to urban clusters of Democrats is quite well suited for the representation of Republicans in Congress."

From the Loser's Bonus- You can see that geography makes a big difference in who benefits. The authors argue that the degree of bonus is correlated with the the concentration of Democrats in cities. 

Longer term, however, pursuing gerrymandering could backfire against Republicans. While geographic trends favor Republicans, demographic trends over the next 10-25 years heavily favor Democrats. If redistricting amplifies the ruling party's lead by providing disproportional voting rights, then if the redistricting cycle reverses from demographic pressure, Democrats could solidify their power for decades to come.

This shows how redistricting favors both parties at different times and places. Sometimes Republicans benefit. Where? 2016. Somewhere Democrats benefit. When? Texas. Sometimes Democrats benefit. Where? 1961. Somewhere Republicans benefit. When? Where? What? Ugh, who cares what the politicians want? It's time to take matters into our own hands!

Expecting politicians to exhibit strategic long term thinking is like economists assuming all humans behave rationally. One might hope a fairer policy would benefit both parties overall, but if not, public policy is for the people not the parties.

Redistricting Rules
There are really only 2 redistricting rules that the supreme court has decreed unconstitutional: racial redistricting and lack of equal population per district. An important caveat is that partisan gerrymandering is often okay, and since racial and partisan redistricting are highly correlated, most redistricting efforts are de facto legal and difficult to challenge in court.

Many states add the desirable constraints requiring boundaries to be continuous (or not arbitrarily splitting) and compact (not too unusual of a shape), but this is usually not a precious definition, And mathematically speaking, there is a virtually infinite number of ways to break up the geometry of state districts. Even with the main constraints being equal population per district and continuity, politicians can fairly easily pick the most aggrandizing district boundaries. How do they do this?

Wikipedia

Packing the Crackers
Imagine a state with 5 districts, where 40% of citizens vote Republican and 60% vote Democrat. Packing is what happens in the top right rectangle above, where one party's voters are concentrated or 'packed' into a couple of districts, limiting their impact and leading to 3 out of 5 districts going to the Republicans.

Cracking, on the other hand, involves splitting and diffusing a party's voters such as the top left rectangle above, leading to the theoretical possibility that Republicans get 0 seats even after receiving 40% of the vote. Either way, the goal is to manipulate district boundaries to the disproportionate benefit of the party in control.

Note, this toy example succeeds in showing gerrymandering under the assumptions of equal population per district and continuity, but these concepts extend to many, if not most, US states.

Mind the Efficiency Gap
Update: Thanks to a comment, I have provided a more direct and intuitive definition of the Efficiency Gap.

How can we detect if partisan gerrymandering has occurred? It might be tempting to simply compare the percentage of votes with the percentage of seats- aka the proportionality of the redistricting process. However, from a legal perspective what matters more is partisan symmetry. As the New York Times reports:

‘‘... the Supreme Court has rejected proportional representation, which the Constitution doesn’t provide for, as a measure of mandating fairness in elections. Instead of dictating that a party with 46 percent of the vote takes 46 percent of the seats, symmetry means that if Republicans win 60 percent of the seats with 46 percent of the vote in one election, then Democrats should be able to win 60 percent of the seats with roughly the same percentage of the vote in another election."

This leads to a concept called the efficiency gap based on a related concept of wasted votes. A wasted vote is any vote that is not for an elected candidate or any vote in excess of 50% for that elected candidate, i.e. a vote that didn't help the winning candidate win. Let W(R) be the wasted votes for Republicans, W(D) be the wasted votes for Democrats, and T be the total votes cast in an election, then the efficiency gap EG can be defined as follows:

EG = [W(D) - W(R)] / T, ranging from 0.0 to 0.5, which simplifies to:

EG = [ D(S) % - 50% ] - 2* [ D(V) % - 50% ], where D(S) is the number of seats allocated to Democrats, and D(V) is the number of votes statewide to Democrats.

In words, the efficiency gap is the difference between the amount of seats won compared with the amount of votes allocated statewide, very similar to a measure of proportional representation. For example, in North Carolina, Democrats won 3/13 = 23% of seats and ~47% of statewide votes, leading to EG = (23% -50%) - 2*(47% -50%) = -27% + 6% = -21%. Any EG (whose absolute value is) more than 8% is considered egregious.

Here's the efficiency gap measure per state where you can see North Carolina and Pennsylvania rank highest:

Azavea

The problem with the efficiency gap is that it doesn't factor in the unintentional geographical clustering of parties. Democrats have been populating urban cities while Republicans have been moving out to the suburbs and the farms. This means that even with no intentional partisan gerrymandering, there would still be a redistricting benefit on average to Republicans, so that Democrats can expect to win less than 50% of the seats even if they win 50% of the votes.

As such, the efficiency gap can lead to many false positives or false negatives by trying to summarize extremely complicated ("multidimensional") geographic and political representation into a single number. This muddles things a bit and gives ammunition to Republicans arguing that the efficiency gap shouldn't be used in court. If Democrats naturally self sort into cities, our hypothetical Republican friend argues, Republicans aren't being partisan hacks; they must gerrymander to protect themselves against geographic unfairness!

Court cases have rarely been settled solely based on the efficiency gap; instead, it is part of an overall argument put forward by those challenging gerrymandered districts. Is there hope for a better way?

Back to the reDrawing Board

As we can see, the lack of mathematical rigor has made arguments for and against gerrymandering literally go on for centuries. Perhaps we should start with some first principles.

1. Should we just give reign to independent commissions?

Probably, but we still need to give them a framework to abide by. Iowa and Missouri offer admirable models; Iowa for its long history and Missouri for its use of a statistical model based on the efficiency gap that was approved in 2018. The idea of following a mathematical formula can be attractive to both the right and the left. Simple rules reduce the ability for politicians to take advantage of a system while increasing the transparency of the process.

2.  Is there a non-partisan argument against competition?

FiveThirtyEight has a great tool for showing redistricting simulations, including what states would look like if they maximized the number of seats where either a Republican or Democrat could win (i.e. the competitiveness of each seat). While neither Democrats nor Republicans will probably like that approach in safe districts, this approach would be best for a democratic system aiming to better represent the views of its citizens, as well as reducing politicians' complacency and incumbency. Missouri's recent amendment requires partisan fairness first and competitiveness second. 

3. Is there a non-partisan argument against proportional representation?

The issue of proportional representation is slightly more complex. As mentioned, the Constitution doesn't explicitly require the number of seats allocated to be proportional with the number of votes; however, intuitively, it seems like proportional representation is the fairest and least biased approach. This might even give 3rd parties a chance to compete with the 2 party duopoly, allowing for better representation of diverse view points. 

Republicans might counter saying that they are geographically disadvantaged and deserve disproportional representation, but the Constitution accounts for geographic representation by giving every state 2 senators, no matter how small. And proportional representation doesn't mean Republicans get no votes; on the contrary it ensures Republicans would always get some representation assuming they get more than 0 votes. 

4. Do we really need compact districts?

You tell me which picture looks more natural and less likely to be abused by politicians. 

https://bdistricting.com/2010/PA_Congress/

A Statistical Approach

If the efficiency gap isn't entirely appropriate, is there a better way of detecting partisan redistricting? A couple of Carnegie Mellon mathematicians seem to think so. "The task then is to evaluate whether a districting not only favors a given political party, but does so to a degree that is atypical for the particular political geography of the state." Their mathematically complex but intuitively simple approach can be outlined as follows:

Define valid districts by equal population, continuity, and compactness. Compare current districts per state by all total valid districts, what is called the total "space" of valid districts in statistical terms. Since the total space is very large, most valid districts will not result from partisanship. Only statistically unusual districts will probably be the result of intentional gerrymandering.

The difficulty is that the total space of districts isn't just very large; it's insanely large, so yuge you couldn't in practice exhaustively search all districts even with the most advanced super computers available. But human ingenuity doesn't stop where search spaces grow exponentially! 

Instead, start with the current districts. Apply millions of small random changes known as "Markov Chains." If your current district appears "among the worst ε fraction of districtings observed in the Markov sequence, and ε is very small, than this would seem to indicate that X0 [your current district] is somehow a very carefully chosen member." Indeed, they prove you would need to run approximately 1 trillion simulations before you get Pennsylvania's current districts! Virtually, statistically, impossible.

Future Projects
Projects such as PublicMapping.Org introduce transparency in the redistricting process by allowing you to create your own districts for any given state. BDistricting.com shows what each state might look like without gerrymandering. Additionally, FiveThirtyEight has some interactive maps that allow you to see various scenarios such as maximizing the competitiveness of races, minimizing the efficiency gap, or maximizing one party's gain.

FiveThirtyEight

It would be valuable for historical analysis, as well as understanding the dynamics, instability, and polarization introduced through the redistricting process, to create a comprehensive time series map from the founding of the US to now of the redistricting geographic boundaries, voting records, efficiency gaps, and other measures across each state.

Additionally, running the aforementioned statistical approach on not only current but historical data sets could further refine this line of thinking. Open sourcing these data and algorithms to the public would provide insight and accelerate research into what has no doubt been one of the greatest distortions of voter intentions in US history.