Xjyuk

Gerrymandering can keep a relatively unpopular party in power for longer than it otherwise would be. Assuming the unpopular party becomes even more unpopular, just how unpopular would they need to be before the stratagem of gerrymandering itself is insufficient to support them?

For example, in 2016 gerrymandering enabled Republican candidates who received 50% of the popular vote to win 9 out of 12 available Congressional seats in North Carolina. That is, half the votes, but 3/4 of the seats and power. And suppose that as long as they hold 3/4 of the power, they'll continue to gerrymander.

Now suppose in the future, the Republicans become more unpopular, and receive only 25% or 10% or even 1% of the North Carolina vote, can gerrymandering alone sustain their hold on the majority of seats, or is there some necessary numeric limit that would eventually be reached?

Note: for the purposes of this question, please ignore other concomitant strategems by which unpopular parties might squeak by.

This is a rather simple mathematical exercise. If you allow me total freedom to draw districts within the current requirements, I can place anyone in any district I want provided they have equal population in the end. Connectedness in two dimensions is not enough of a barrier to stop this. In that case, my best bet is to fill as many districts as possible with 50%+1 of my supporters, and fill in the rest with my opponents. Since at least half the population of each district I win must consist of my supporters, we can easily see there is an upper limit on how many districts I can win:

A party with x% of the vote cannot win more than 2x% of the districts no matter how they are drawn.

In practice there's no way I can reach this limit--no court in the land would allow me to draw the kind of tortured districts needed for arbitrary assignment. 50%+1 is also nowhere close to safe--I'd need a small buffer in my districts so that changing demographics and opinions don't turn it into a gerrymander against me. I'd guess that overall this limits one's practical chances to 1.5x%, but this just an estimate, not a mathematical truth.

In theory, if the stars align perfectly, one can gerrymander a 50-50 vote to win 11 out of 12 districts. This can be done by drawing the district boundaries so that one district has 61% of voters supporting your opponents, and the other 11 have only 49% supporting your opponents.

In practice, it will come down to how tightly packed, geographically, your opponents are. If they are evenly spread, then it becomes much more difficult than if they are densely packed in a few geographic areas. Thanks to a combination of voter registrations (where the state knows voter affiliations in each house), and cheaper computing power allowing for more complex modelling, a willing party can find a way to optimise the boundaries for their benefit.

The problem here is that "one person one vote" can be based on residents rather than citizens or voters. So if you could assign people purely arbitrarily, you could fill up your districts with non-voters such that only a small number of voters are required. In theory, one voter and eight hundred thousand non-voters per district would work. Pack all the other side's actual voters into one district (no non-voters and none of your voters).

However, you then run into a few problems.

1. It's not the number of federal House seats that determines your ability to gerrymander. It's the number of state legislative seats. So you need more than just twelve federal seats. You need a larger number of state seats.


2. You can't gerrymander statewide races. So to make this work, you have to disempower the governor's ability to veto a districting plan.


3. Most states don't have enough non-voters to make this work.


4. You can't actually assign people arbitrarily per district.

Realistically, this would never work. But it is theoretically possible with just a few hundred voters given sufficient non-voters.

In actuality, Republicans in North Carolina received slightly more votes than Democrats. But instead of winning seven to six, they won ten to three in North Carolina. But this didn't overcome the Democratic gerrymander in California, where Republicans won about 33% of the vote but only 11% of the seats. That's a surplus of twelve for the Democrats. Even netting out the three for the Republicans from North Carolina, that's still an advantage of nine seats for the Democrats from those two states.

Apparently in the last House election, the gerrymanders almost exactly cancelled out. The Democrats won about as many House seats (54%) as their share of the vote (53.4%). Which is surprising because Democrats face a natural handicap in that their voters are more concentrated than Republican voters.

Source: Wikipedia from Johnson, Cheryl L. (February 28, 2019). "Statistics of the Congressional Election of November 6, 2018". Clerk of the U.S. House of Representatives.