As election day has approached, I’ve increasingly heard the phrase “blue wave” thrown around in news articles, forums, and even everyday discussions. The term is commonly understood to mean that high Democratic turnout in the midterms could lead to significant Republican losses in the House. It’s clearly true that unusually high voter turnout within a single party will help that party’s chances on election day, but there’s a bit more to it than that. The blue wave mantra extends beyond that to imply that Republicans’ are especially susceptible to losses in the house due to the widespread gerrymandering of congressional districts in their favor.

Even aside from it’s relevance to a blue wave, gerrymandering is a concept which seems to be in the news almost constantly. The Supreme Court very recently rejected the appeal of a Pennsylvania Supreme Court ruling that the state’s congressional districts violated the state’s constitution because they prevented elections from being “free and equal.” Last spring, in Gill v. Whitford, the Supreme Court also decided not to rule that Wisconsin’s legislative map was an unconstitutional gerrymander, and there are currently ballot initiatives in Colorado, Michican, and Utah to create independent commissions to draw congressional district maps in those states.

It’s difficult to completely separate any discussion of gerrymandering from politics, but we’ll try to mostly do that in the remainder of this article. The examples that we’ll use are very simplified and aren’t meant to make any direct statement about current politics. The Republican and Democratic party names are used because of their relevance to explaining the “blue wave” terminology, but the main point is to explain the general principles behind gerrymandering. We’ll explain in simple terms how gerrymandering works, and how it can be thought of as a strategy that exchanges increased risk for increased reward. The increased risk associated with gerrymandering leaves the advantaged party vulnerable to unexpectedly large voter turnout from the other party, and this is the core idea behind the blue wave. The concept is very intuitive once you see it in action, and we have an interactive visualization below which helps understand the exact hypothetical mechanics of a blue wave.

What is gerrymandering?

Gerrymandering itself is a fairly simple concept: it corresponds to drawing voter districts so that election outcomes are likely to benefit one political party over another. The practice is often associated with strangely shaped voter districts, and the name “gerrymandering” is itself a portmanteau and reference to the salamander-shaped Massachusetts senate district drawn by Governor Elbridge Gerry in 1812.

Although the shape of gerrymandered districts might be their most distinctive feature, this is really just a side-effect of drawing districts which consist of precisely controlled ratios of Democrat to Republican voters. The convoluted lines are strategically drawn so that one party is likely to win as many districts as possible.

The physical layout of gerrymandered districts is very interesting in its own right, but it’s mostly unimportant for understanding how different districting strategies affect the likely outcomes of elections. Let’s walk through a simplified example that illustrates how gerrymandering can result in one party being significantly overrepresented.

Imagine a situation where you have 12 Republican voters and 24 Democratic voters that need to be divided into six different winner-takes-all districts which each contain six voters. There are many different ways that you could distribute these voters between the districts. One way would be to put two Republicans and four Democrats in each of the districts. This sort of homogeneous distribution would result in the Democrats winning all six of the districts because they would have the same 4:2 majority in each of them.

Another strategy would be to have two districts composed of all Republicans and four districts composed of all Democrats. This segregated distribution would result in Democrats winning four districts to the Republicans’ two. The 4:2 ratio of districts here matches the ratio of actual voters between the two parties, and it therefore results in more proportional representation than the homogeneous approach.

An alternative strategy would be to have three districts composed of solely Democratic voters, and then three districts that each have four Republicans and two Democrats. The election outcome in this case would be that the Democrats and Republicans each win three districts. This is representative of how gerrymandering works; the districting strategy was carefully constructed to maximize the representation of a single party (the Republicans in this example). The basic idea behind the strategy is to win narrow victories in as many districts as possible while purposely losing the remaining districts by much larger margins.

In this example, the Republicans can win anywhere from zero to three districts depending on how people are divided up between the districts. The key thing to take away here is that the more extreme outcomes correspond to the proportionally overrepresented party winning their districts by narrow margins. We’ll take a look in the next section at how these narrow margins can result in large deviations from expected outcomes.

The Risk vs. Reward Tradeoff

In order to explore how gerrymandering affects risk, let’s look at a slightly more realistic example. We’ll extend the number of districts to 20 and consider the composition of the districts in terms of percentages instead of discrete voters. The default settings below place the percentage of voters that are Republican at 42% and assume a gerrymandered districting strategy. This strategy allows the Republicans to win 80% of the districts, numbered 1-16, by a narrow 52.5%/47.5% margin.

You can increase the Democratic voter turnout in each district by dragging the slider labeled “Extra Democratic Voter Turnout.” What you’ll see is that there comes a point where the narrow Republican victories can all suddenly flip if there’s a relatively small surge in the number of Democratic voters. You can compare this to the segregated strategy where the Democratic voter turnout has almost no impact on the overall election results.

One could also imagine a variety of strategies which fall between these two extremes of trying to win 9 districts with the segregated strategy and 16 with the maximally gerrymandered strategy. The segregated strategy can be thought of as the least risky strategy because the outcome is largely independent of the voter turnout. For each additional district that the gerrymandered strategy attempts to win, it narrows the margins and makes the strategy more vulnerable to high Democratic turnout. The higher reward strategies come directly at the expense of higher risk.

Conclusion

To sum it up, the idea behind the blue wave terminology is that the Republicans have narrow leads in a number of districts which could be flipped en masse in the event of unexpectedly high Democratic turnout. Gerrymandering involves sacrificing larger margins of victory in each district in exchange for a higher number of expected victories, and these margins can disappear to variations in voter turnout or other similar factors. This makes gerrymandered strategies inherently more risky than strategies which result in something closer to proportional representation.