Chris has graciously allowed me to submit a guest post, so I thought I’d do one about gerrymandering and why it’s particularly fascinating for this election cycle.

Those reading the title might expect me to say the devil’s bargain is tampering with the democratic process, or some other moral argument against gerrymandering. While there are lots of such arguments with lots of merit that should be debated (and indeed, several courts are considering that very point as we speak), this will not be one. It’s a purely inside-baseball deep-dive into the dark art of gerrymandering itself, and the numbers and statistics that are its bread and butter, along with my humble notes about some interesting phenomena that might occur this cycle as a result of the current map.

So what exactly is the devil’s bargain then? It is this: gerrymandering allows you to win close elections, but makes you more susceptible to being washed out in wave elections. The basic idea of gerrymandering is that you make your opponent “waste” votes by packing his voters into a few districts. And then, you spread your voters around as thinly as possible, capturing 51% of the vote in as many districts as possible. That’s why in Republican gerrymandered states, Dem strongholds in cities frequently rack up 90% Dem majorities (in fewer districts), while Republican districts skate by with 55% majorities or less (in more districts). At the end of the day, it doesn’t matter what your vote totals are as long as you’re at >50%.

That’s the good side of gerrymandering. The downside is evident by looking at the above numbers closely: thanks to packing, the Dems will never lose their 90% majority seats. Meanwhile, if the election swings 5%, the Republicans lose *all* their seats. And that’s the Devil’s bargain: the more aggressively you spread your voters to maximize your seats in regular elections, the fewer votes you have to serve as a buffer against a wave.

Another phenomenon to understand is that this is not a linear process. In our simplified example above, the Republicans lose *no* seats until the Dems hit 55%, and then, they’ll lose *all* of them. IOW, the Republicans in this example have a “firewall” that can withstand up to a 5% wave, but then get entirely washed away with anything more than that. Of course, this is a hypothetical example, but it holds in the real world.

When politicians decide their gerrymander, they decide how aggressive they want to be, and how much “reserve” they put in each district to withstand wave elections, population shifts (remember districts have to hold for 10 years), etc. Oftentimes they even take into account the actual politician holding the seat right now. If he’s a popular incumbent who’s expected to stay in office for 10 years, then he needs less reserve. He might even have enough bipartisan support that you can make his district minority Republican. OTOH, if it’s a district with a new Congressperson, or an old guy who’ll likely retire in a few years, then you might put a few more Republicans in their districts to help them out. Of course, there are backroom negotiations for all of these: while everyone agrees in theory to spread out voters to maximize district wins, each individual politician wants an easy district, with tons of supporters, which means sometimes a powerful Congressman gets to keep a bunch of voters he doesn’t need, just so he can sail through his elections.

At the end of the day, all of these individual decisions (and I do mean individual: districts are frequently drawn down to the block and sometimes individual house level; often to exclude a popular incumbent from a district that contains his vote base) lead to the national map that we now have.

So with that background, just how does that national map look? Is there a linear progression of districts? That is, for each 1% gain in vote share, does a party’s district total increase linearly? Is it exponential? Or does the firewall concept I described above apply?

In order to answer this question, we have to first ask: at each level of partisan breakdown of the national vote, how many districts will the Dems hold? And for each increase of 1% in the vote total, how many additional seats will the Dems get? If there is no gerrymandering, this should follow a normal distribution. That is, you’ll see a large number of districts change hand right around the 50/50 mark and fewer districts as you get to the extreme. For example, if you’re at 90%/10%, there aren’t many more districts left for you to win, so each extra percentage point increase in your vote total won’t bring all that many additional seats. At 50/50, there should be a ton of districts that will swing with just small changes in vote totals. This is what you’d expect without any gerrymandering.

But how would a graph look in the firewall concept above? In that hypothetical example, between 50%-54% vote share, the Dems get zero additional seats with each 1% increase in vote share. But at 55%, they get *nine* with the next 1% increase in vote share.

Can we make similar calculations for the national map? Turns out we can. The Cook Political Report publishes a commonly used metric, called the Partisan Voting Index (PVI). This measures partisan lean compared to the national average. So for example, a district that is D+5 leans 5 percentage points more towards Democrats than the national average. In an ideal world, all districts would be +0, i.e. their partisan lean is no more or less than the national average. Which means the PVI is a useful indication of how badly gerrymandered a district is (although it’s not perfect; there are other factors besides gerrymandering that affect PVI. For example an incumbent who’s popular with both parties might get more votes than the national average, which will give him a large PVI). In graph 1, I’ve taken the PVI of each district and plot it on a graph. As the Democratic vote total goes from -50 (i.e. they underperform the national average by 50 points) to 0 (i.e. right at the national average) to +50, you can see how the total number of districts the Democrats win changes as their national vote total changes. At 0, you can see that the Democrats don’t get a majority, which is confirmation of the Republican gerrymander. Indeed, they aren’t predicted to get a majority until they hit about +5%.

Next, we get to graph 2, the key graph. This shows the number of additional seats the Democrats can expect to win with an additional 1% increase in vote share *at each level of vote share*. I believe a clear firewall effect can be seen, and to see it, I’ve added annotations.

The blue dotted line shows a normal curve that we should expect to see if there was no gerrymandering. And in the extreme left and right, the graph largely conforms to this. However, in the middle, where most gerrymandering takes place, you’ll see a marked difference. At the zero point (i.e. 50/50 vote share), the number of districts that change hand decreases. To the left of that point, you can see that the number of seats lost by Dems drastically decreases for a few percentage points, until their firewall breaks. After that, as you follow the graph left, the number of seats lost drastically increases with each point until it settles into the expected normal curve beyond the gerrymandered seats. That means the seats within the green oval have been gerrymandered to withstand a wave election. To do so, the districts in the red oval have been made *more vulnerable* than they would normally be. This is the devil’s bargain inherent in all gerrymandering.

How about the Republicans? If you follow to the right of the zero point, the Republican gerrymander can be seen as well. For the first 5-7% vote shift, while there are districts changing hands, the number of such districts is less than expected, thanks to gerrymandering. However, the price for that gerrymandering is that the districts slightly to the right of that (in the red oval) become extraordinarily sensitive to a wave. Which means that if Dems are able to push beyond the wall, they may see *increased* number of districts falling their way. Normally, it would be the opposite: as you get further from 50/50, the law of diminishing returns sets in and you see fewer pickups.

Based on this graph, I assert that the Republican gerrymander breaks between about 8-15% wave election. While the firewall isn’t absolute (districts do change hand even below those percentages), the number of districts that change drastically increase once the firewall is broken, more than if the gerrymander wasn’t there in the first place. Which means the two most likely scenarios is that either the Dems fail to breach the firewall and remain in the minority (albeit with a smaller gap), or they break the firewall and gain a large majority. Ironically, it’s less likely that they get to a bare majority and stay there.

So far, the polls and results seem to point to the Dems being at the cusp of breaking this firewall. Generic Congressional ballots have had the Dems up 6-12 points. Meanwhile, in special elections thus far, Dems have been running about 16% ahead of their previous performance. This has held even in high-turnout elections like the AL-Sen and the PA house district races.

In summary: until about 8% advantage, the Dem wave will be crashing against the Republican gerrymander. While that may be enough to stagger to a tiny majority, it’s also very possible (maybe likely) they end in the minority even with that voting advantage. However, from 8% to 15%, it turns into a tsunami, where even relatively small increases in Dem voting percentages will yield enormous numbers of districts. If the Dems can push beyond that barrier, thanks to the Republican gerrymander, the Dems may be looking at a very, very comfortable majority, one they wouldn’t have had if the Republicans left their districts alone. The polls suggest they may be right around the cusp. Which means after all these years, the Devil may finally be knocking at the Republicans’ doors, collecting his due…