In the United States, both state legislative and congressional districts are designed by politicians. These politicians, especially in the Republican-controlled states (this has only been true since 2010 or so) tend to design districts to give a clear and consistent advantage to their party. The canonical example of this is North Carolina (current [smoother] district lines):

The x-axis indicates the district, the y-axis shows the two-party Democratic presidential vote. Given the highly sorted party system currently existing in the United States, the presidential vote functions as a very good proxy for House candidate vote and is more appropriate here than House vote since the candidates are the same in every district. As one can readily see, in North Carolina, Democrats are packed into only three out of thirteen congressional districts, even though they won over 48% of the two-party presidential vote in both 2016 and 2012. Only in 2011 were the lines redrawn to favor the Republicans (and they will continue to favor the Republicans for a long time), before, they favored the Democrats since the 1890s.

Given that not all gerrymanders are created equal, several ways have been proposed to measure this phenomenon.

I. Insufficiency of commonly used methods

One way has been to compare the difficulty of recapturing the majority of the seats relative to winning the majority of the two-party vote in a state by looking at the difference between the presidential vote of the median district and the statewide presidential vote. However, one of the most gerrymandered states by this measure is Tennessee, which is a 60%+ Republican state with two Democratic seats (out of nine total)! Massachusetts (a 60%+ Democratic state with the same number of seats as TN) does not have even a single Republican seat! Yet, nobody can seriously call Massachusetts gerrymandered against the Republicans. Tennessee’s creation of more Democratic seats almost necessitates a higher difference between the median seat and the state due to more Democratic voters having to be taken away from the state’s median seat into the Democratic-held seats. Thus, the median district approach cannot be used as a serious way to measure gerrymandering, as it only looks at one district-the median one.

Another way to measure gerrymandering has been some kind of way of comparing share of seats won by v. share votes cast for a party. This is also a very flawed method.

The problem with these approaches is that they cannot distinguish between this (super-weak Democratic gerrymander in an evenly tied state with ten districts):

and this (strong Democratic gerrymander in an evenly tied state with ten districts):

But pretends there are giant differences between this (super-weak Democratic gerrymander in an evenly tied state with ten districts):

and this (super-weak Republican gerrymander):

As you can see, the problem with this approach is that the most gerrymandered maps by this measure will inevitably be dummymanders -that is, maps in which the party drawing the districts is so thinly spread out, if the popular vote shifts uniformly to the opposing party just a little, the map will look identical to a gerrymander designed by the opposing party.

In any case, any gerrymander has to be judged on two criteria: seat maximization and safety. There is a direct trade-off between the two (as thus, for an evenly tied state in which any and all district boundaries are permitted):

Notice that the curve is bowed in. However, in practice, the difference between a two point and a ten point presidential win margin is worth much more in terms of a House member’s win probability than that between a thirty point and fifty point presidential margin. Given this, the top and the bottom portions of the y-axis should be compressed and the middle expanded. With the axis like this, the curve would be bowed out, and the point of most correct gerrymander be placed at the outermost point of the curve.

Such curves should be designed for every state in the union with a reasonable number of House districts to test for gerrymanders there. Generally, the optimal average win margin for a favored party (that is, one that does not waste votes, but still keeps seats reasonably safe) is probably around ten points for an evenly tied state. Any good gerrymander should be directly on the possibilities frontier (as my strong D gerrymander graph with red bars is), not within it (as my super-weak D gerrymander graph with red bars is).

Ideally, a gerrymander should have

  1. Zero seats flipping on the presidential level between elections outside wave years (on the logic that it is better to have a bird in the hand than two in the bush)
  2. Total unity between the House member’s party and the party of the presidential candidate that wins the district (the state that is easily farthest away from fulfilling this ideal is Minnesota; the closest states to this ideal are, as far as I can tell from a quick glance, Maine, Missouri, and North Carolina).
  3. Maximized number of seats given a state’s partisan lean

Goals 1. and 3. are obviously inconsistent if a state hugely changes partisanship between elections.

Pennsylvania failed all the criteria in 2016 (it had split districts both ways, seats flipped in presidential vote between 2012 and 2016, and obviously it didn’t maximize GOP seats in 2016, and probably not in 2012, either), but it’s a pretty clear GOP gerrymander regardless. Wisconsin blatantly failed all the criteria in 2016 and probably failed the third criterion (though not the second) in 2012, though it was a very clear pro-GOP gerrymander in 2012. Michigan and Ohio satisfied all the criteria in 2012, but did not satisfy the last criterion in 2016, due to the state changing partisan lean between those years and there being obvious Democratic seats in both states which could be removed in 2016. North Carolina clearly satisfied all the criteria in 2016, but had some disunity between House member’s and district presidential candidate victor’s party in 2012. Texas satisfied none of the criteria in either 2012 or 2016.