Gerrymandering Math
I ran across this summer school recently and read this white paper, and while I'm happy this sort of work was getting done I was struck by how shallow the analysis there seemed to be.
So I started thinking about what sorts of simple improvements could be made, that could still be computed automatically rather than needing to be hand-drawn or specified.
The first point that they mention several times is the idea that boundaries of cities, coastlines, and state borders can cause massive increases in perimeter without being any more suspect when identifying gerrymandering. This seems like an easily solvable problem, and I'll address a couple methods for tackling it here.
First, is to consider districts as being partitions of the convex hull of the region in question, rather than partitions only of the region. For each district in the region, include with it any point within the convex hull that is closer to that district than any other district. This sounds a little complicated, so here's an ugly picture I drew in MS Paint:
By any methodology used in the study (for example, Reock measure which compares the district's perimeter to the smallest circle that contains the district; or Schwartzberg which measures the ratio of the district's area to that of a circle with equal perimeter) this district will look like a hugely gerrymandered mess.
However when extended to being a partition of the convex hull of the state, more than half of the district's perimeter disappears while it's area substantially increases.
Here's a second idea: draw a straight line through any district border that is defined by water or the border of the region being districted (perhaps use the convex hull here as well) and use this for calculating the perimeter.
One method proposed in the white paper is to compare the compactness of the district to the overall compactness of the region. However this is a bad fit for a district like Florida-14 above: this is a small piece of noncompact land within a larger, more generally compact state. Consider also the northwest end of Oklahoma, the southeast bayous of Louisiana, or Manhattan island in New York.
My next thought is that gerrymandering essentially implies a purposeful bias in selecting district borders. This purpose could be detected, for example by looking at semi-local demographic data. It's not clear to me how easily available this data is but it must be for the districting process to be possible in the first place.
Here are a couple of thoughts on detecting whether the district seems to have unusual demographics relative to the surrounding area:
Compare the population (say, mix of ethnicities, major party vote share) of the district to its convex hull. This is much more difficulty with cities, since a rapid change in demographics is likely when entering an urban area, and it might be appropriate to draw district lines along these lines.
So a second pass at the idea: Consider a square region the same size as the district extending diagonally in each cardinal direction from the center of the district:
This district has a CPVI of D+21, but the district to the east (6th) is R+9, to the north and west (3rd) is R+14, surrounding the northern tip is the 4th district at R+19, and to the southwest are districts 10 and 11, at R+6 and R+11 respectively. The combination of ridiculous non-compactness with vastly different demographics than surrounding districts suggests that this is clearly gerrymandered for political purposes.
Also consider the similarly non-compact 22nd district, which is sits at D+3 and is surrounded by districts 20 (D+29), 21 (D+10), and 23 (D+9)--this is a competitive district surrounded by non-competitive districts--honestly it kind of looks like district 20 is sinking its fangs into the territory to drain local democratic support by 7 points.
Contrast with California's 22nd district, which has a CPVI of R+10, but sits in between some very diverse and reasonably drawn districts: CA-4 (R+10), CA-16 (D+7), CA-21 (D+5), and CA-22 (R+15). This district has a population that seems contiguous with the surrounding area, even with its weird outline (some of which is also drawn from the mountain range.) You can also see this in the districts of LA, which have a voting index that seems to correspond pretty strongly to whether they're a central urban area.
An alternative to this "semi-local" information would be to look at something like global information. If one comes into districting with the explicit goal of making as many competitive districts as possible, then something like FL-22 makes sense--though this also would result in a much more volatile political system, where for example the house could change from a supermajority in one direction to a supermajority in the other within one election cycle. Whether you see this is a feature or a bug probably depends on your perspective.
Alright, that's it for me spitballing. While dealing with coastlines and city borders still seems easily solvable, I do think this is a complicated problem and figuring out what the proper reasons to make districting choices are is a necessarily collaborative political process.
Of course we could also just have proportional legislatures, where parties have lists of candidates and get to put a number in corresponding to the share of the vote they recieved. I like the idea of cutting down on local special interests in general, and I LOVE the notion of the green party getting consistent seats in congress, but there are certainly problems with individual accountability and the escalation of political party machinery.
So I started thinking about what sorts of simple improvements could be made, that could still be computed automatically rather than needing to be hand-drawn or specified.
The first point that they mention several times is the idea that boundaries of cities, coastlines, and state borders can cause massive increases in perimeter without being any more suspect when identifying gerrymandering. This seems like an easily solvable problem, and I'll address a couple methods for tackling it here.
First, is to consider districts as being partitions of the convex hull of the region in question, rather than partitions only of the region. For each district in the region, include with it any point within the convex hull that is closer to that district than any other district. This sounds a little complicated, so here's an ugly picture I drew in MS Paint:
By any methodology used in the study (for example, Reock measure which compares the district's perimeter to the smallest circle that contains the district; or Schwartzberg which measures the ratio of the district's area to that of a circle with equal perimeter) this district will look like a hugely gerrymandered mess.
However when extended to being a partition of the convex hull of the state, more than half of the district's perimeter disappears while it's area substantially increases.
Here's a second idea: draw a straight line through any district border that is defined by water or the border of the region being districted (perhaps use the convex hull here as well) and use this for calculating the perimeter.
One method proposed in the white paper is to compare the compactness of the district to the overall compactness of the region. However this is a bad fit for a district like Florida-14 above: this is a small piece of noncompact land within a larger, more generally compact state. Consider also the northwest end of Oklahoma, the southeast bayous of Louisiana, or Manhattan island in New York.
My next thought is that gerrymandering essentially implies a purposeful bias in selecting district borders. This purpose could be detected, for example by looking at semi-local demographic data. It's not clear to me how easily available this data is but it must be for the districting process to be possible in the first place.
Here are a couple of thoughts on detecting whether the district seems to have unusual demographics relative to the surrounding area:
Compare the population (say, mix of ethnicities, major party vote share) of the district to its convex hull. This is much more difficulty with cities, since a rapid change in demographics is likely when entering an urban area, and it might be appropriate to draw district lines along these lines.
So a second pass at the idea: Consider a square region the same size as the district extending diagonally in each cardinal direction from the center of the district:
This district has a CPVI of D+21, but the district to the east (6th) is R+9, to the north and west (3rd) is R+14, surrounding the northern tip is the 4th district at R+19, and to the southwest are districts 10 and 11, at R+6 and R+11 respectively. The combination of ridiculous non-compactness with vastly different demographics than surrounding districts suggests that this is clearly gerrymandered for political purposes.
Also consider the similarly non-compact 22nd district, which is sits at D+3 and is surrounded by districts 20 (D+29), 21 (D+10), and 23 (D+9)--this is a competitive district surrounded by non-competitive districts--honestly it kind of looks like district 20 is sinking its fangs into the territory to drain local democratic support by 7 points.
Contrast with California's 22nd district, which has a CPVI of R+10, but sits in between some very diverse and reasonably drawn districts: CA-4 (R+10), CA-16 (D+7), CA-21 (D+5), and CA-22 (R+15). This district has a population that seems contiguous with the surrounding area, even with its weird outline (some of which is also drawn from the mountain range.) You can also see this in the districts of LA, which have a voting index that seems to correspond pretty strongly to whether they're a central urban area.
An alternative to this "semi-local" information would be to look at something like global information. If one comes into districting with the explicit goal of making as many competitive districts as possible, then something like FL-22 makes sense--though this also would result in a much more volatile political system, where for example the house could change from a supermajority in one direction to a supermajority in the other within one election cycle. Whether you see this is a feature or a bug probably depends on your perspective.
Alright, that's it for me spitballing. While dealing with coastlines and city borders still seems easily solvable, I do think this is a complicated problem and figuring out what the proper reasons to make districting choices are is a necessarily collaborative political process.
Of course we could also just have proportional legislatures, where parties have lists of candidates and get to put a number in corresponding to the share of the vote they recieved. I like the idea of cutting down on local special interests in general, and I LOVE the notion of the green party getting consistent seats in congress, but there are certainly problems with individual accountability and the escalation of political party machinery.