The Supreme Court’s Math Problem

March 29, 2019 3:12 PM

Fixing partisan gerrymandering requires some technical calculations. That’s why the Metric Geometry and Gerrymandering Group filed a mathematicians’ brief to better define the problem—and the solution.

The Slate piece is by Metafilter's own Jordan Ellenberg.

posted by eirias (27 comments total)

Mathematicians are like the Ents in The Lord of the Rings—we don’t like to get involved in the mundane conflicts of state, which are out of sync with our slow timescale. But sometimes (and I’m still inside this Ent simile, by the way), events in the world so offend our particular interests that we have to lumber in.

I’m now imagining mathematicians flooding the Supreme Court.
posted by GenjiandProust at 3:49 PM on March 29, 2019 [10 favorites]

This week's Five Thirty Eight podcast on this is also excellent. Moon Duchin from Tufts/MGGG is beyond fantastic. I would listen to her podcast every week if she had one.

Shotgun on the stage name Emcee MCMC.
posted by Telf at 3:52 PM on March 29, 2019 [4 favorites]

Moon Duchin was my roommate’s calculus instructor and is an excellent person in addition to doing this cool work!
posted by mai at 4:00 PM on March 29, 2019 [4 favorites]

Districts should be mathematically calculated to have the same population with minimum boundary length FULL STOP

Of course, this requires accurate census data, which is why the US 2020 census has been under attack for years.
posted by krisjohn at 4:25 PM on March 29, 2019 [6 favorites]

...sometimes events in the world so offend our particular interests that we have to lumber in

I see what he did there!
posted by Insert Clever Name Here at 5:06 PM on March 29, 2019 [3 favorites]

Districts should be mathematically calculated to have the same population with minimum boundary length FULL STOP

Do you want Constitutionally-mandated Republican minority rule for decades?

Because that's how you get Constitutionally-mandated Republican minority rule for decades.
posted by burden at 5:08 PM on March 29, 2019 [7 favorites]

You can see a different but similar set of mathematical arguments over at Planscore. That's a website by (MeFi's own) Mike Migurski that objectively scores a districting plan by several simple statistical measures of "fairness". The simplest one to explain is "Partisan Bias", which in the linked example says that Republicans get 26.9% extra seats in North Carolina if the vote goes 50/50. The "Efficiency Gap" metric is a good measure of votes wasted and gets to measuring exactly what designers of a gerrymandered map intend to do.

Unfortunately the Supreme Court chose to ignore these measures in last year's court cases when they refused to really rule on the gerrymandering case. Particularly disappointing with Chief Justice Roberts dismissing the mathematical measures as gobbledygook, as if one of the chief intellectuals in US government could pretend to be contemptuous of academic arguments. Maybe this case will go differently; North Carolina's map is so egregiously fixed there's not much room for argument.

I might add that while mathematics and geometry are useful for designing districts, they aren't by any means the only necessary tools. There are plenty of reasons to draw districts that are a little funky or off the most mathematically perfect shapes. For instance you generally don't want to cut a town in half with a district line; districts are supposed to represent constituents with something in common demographically. Also sometimes we draw districts deliberately to achieve political ends. For instance the Unholy Alliance in the 80s and 90s where Black Democrats cooperated with White Republicans to draw a few guaranteed-Black districts (in exchange for which the Republicans got a few guaranteed-Republican districts).

I'm super worried about what happens when machine learning tools are applied to drawing 2020 districts. Without a legal restriction on what politicians can do it could get very sophisticated and very ugly.

Voters should choose their leaders; leaders should not choose their voters.
posted by Nelson at 5:10 PM on March 29, 2019 [19 favorites]

Not to accuse any of the august judges of the U.S. Supreme Court of partisanship, but I bet this analysis would've been more broadly convincing to the judges if the mathematicians had included examples where the Democrats were doing the gerrymandering (contra North Carolina) and where Republicans were winning all the seats even with a fair vote (contra Massacheushoweveryouspellit).

I had a situation today where someone asked a woman who's my colleague a question, was given the answer, and then turned to me and asked exactly the same question, so I appreciated these bits in the article:

He was asking a question that had just been answered, a moment before, by Elena Kagan. ... Elena Kagan, as in all the recent gerrymandering cases, is the only justice who seems to have fully grasped what the two sides are asking for. She lays it out very clearly, as well as any math professor could—and then the rest of the court carries on as if she hadn’t spoken.

A question: Could the method they used be called bootstrapping? I'm vaguely familiar with this stuff, and that's the one word I know.

(I realize that I'm way behind on this, but I've been wondering for a while how you'd determine fair districts. This is brilliant! Obvious in retrospect, but no less brilliant for it.)
posted by clawsoon at 5:34 PM on March 29, 2019 [2 favorites]

MCMC is not bootstrapping but it has the same feel, letting you approximate a distribution by generating a bunch of samples according to some scheme.
posted by vogon_poet at 5:48 PM on March 29, 2019 [4 favorites]

I'm watching the animations at Planscore. I don't know what explains the lack of action in the Dakotas, but good on them.
posted by clawsoon at 5:52 PM on March 29, 2019

I really wish any of this mattered, if it did Kennedy wouldn't have punted before retiring, and maybe we could trust that there's any other possible outcome other than the court striking down Maryland's map while upholding North Carolina's. The math is interesting, or would be in a world where the court was at all interested in facts or operated in good faith. As is, it's just a depressing reminder that we don't live in that world, and won't for decades.
posted by T.D. Strange at 8:06 PM on March 29, 2019 [1 favorite]

Districts should be mathematically calculated to have the same population with minimum boundary length

Boundary length is only a proxy for other things that we like. We imagine that a compact district represents a group of people that are reasonably similar to one another (which would be a fine heuristic if people were like solutes in a medium or something), and that a map of all compact districts minimizes the amount of possible funny business a map-drawing authority might get up to.

But really, a map-drawing authority could still push around Voronoi centers until their political opponents have been suitably packed and cracked. It's not a panacea.

I think there is a mathematical way to draw districts that more directly answers to the concerns that people have when they ask for compact districts. I haven't worked out all the details, but the seed of the idea is running a clustering algorithm on (blocks of) people, subject to the constraint that each cluster has to have the same number of people, and (of course) that each district is a single connected shape. Because people live in communities of weird shapes, this method will probably result in weird shapes... but that's fine, because the shapes themselves aren't the important part, it's who gets put with who. I think that for this sort of method to comply with the Voting Rights Act, it can't just be ignorant of who lives where as e.g. minimum split line is. It needs to have information about communities of interest so the people inside them can get clustered together.
posted by a snickering nuthatch at 8:08 PM on March 29, 2019 [8 favorites]

> "Districts should be mathematically calculated to have the same population with minimum boundary length FULL STOP"

"Assume a spherical cow circular electorate …"

I know, American Exceptionalism, not-invented-here, etc. - but it's at least a partially-solved to-a-greater-or-lesser-degree problem in many other democracies. The basic rules are usually something like (to summarise from the Australian Commonwealth Electoral Act of 1918 & elsewhere):

• allocate seats to states in proportion to their population (sometimes with a fixed minimum for less-populous states),
• set limits on the allowable variation in population within each seat of a state,
• group together, as far as possible, "communities of interest" (economic, social and regional), with similar "means of communication and travel" bounded by "physical features and area", into the same electorate; and
• ensure the government "has no power to reject or amend the final determination" i.e. electorates/divisions are drawn by, as far as possible, an independent & non-partisan body.

Of course, all that only works if you can meet that last requirement. The Westminster-style tradition of a fiecely independent public service has (generally, with some notable exceptions) worked for that so far here, but I suspect something will have to be done to either strengthen that or take it out fallible/corruptible human hands sooner or later.

That would probably involve, as hinted at by Jpfed, drawing boundaries based on a best-fit of several clustering algorithms, each based on broad communities of interest - typical local travel, shopping, service delivery, etc. - as well as geographic boundaries. In fact, that's more-or-less how the AEC and others do it now.
posted by Pinback at 8:33 PM on March 29, 2019 [4 favorites]

this is like an "executive summary", is there a good representative paper with actual math and/or algorithm pseudocode?
posted by scose at 9:36 PM on March 29, 2019

This is an interesting issue because you have people simultaneously arguing that the mathematics are too complex to generate fair districting at the very same time people are using the same mathematics to generate reliably gerrymandered districts.
posted by JackFlash at 9:44 PM on March 29, 2019 [10 favorites]

This one seems representative and is clear.
posted by vogon_poet at 9:45 PM on March 29, 2019 [2 favorites]

the problem is not that the republican appointed justices dont get the issue, or are misinterpreting plaintiffs' claims for relief as a demand for proportional represenation. the problem, as with all political problems in america today, is that one side is not acting in good faith. they know exactly that republican gerrymanders are effectively depriving people of the franchise. but they like that because they are republican partisans.

mathematicians' briefs are not going to fix that. it's cute, but i'm sorry. former dubya staffer and trump goon brent kavanaugh doesnt give one shit about mathematicians' briefs. even entertaining the notion that this is a fair contest of ideas, that neil gorsuch would get on board if only we could come up with a workable plan is ludicrous and frustrating.

only bare knuckle politics and winning fucking elections at all costs (despite the handicap that currently exists) will work. just like the dems did last year. but even then, we're still boned in the senate and the electoral college.
posted by wibari at 10:16 PM on March 29, 2019 [13 favorites]

FYI, FiveThirtyEight's Gerrymandering Project has a pretty interesting tool for exploring the effects of alternate district-drawing schemes at the state and national level. I kind of like the straightforward logic of the "make districts compact while following county lines" plan, which makes the House marginally more competitive, but on a purely aesthetic level the "make districts compact with an algorithm" map is striking in its stained-glass beauty.
posted by Rhaomi at 11:55 PM on March 29, 2019 [2 favorites]

I liked the fair division approach, although it is explicitly a two party approach. Turns out that if you iterate the process of (party A draws map) (party B chooses exactly 1 district to keep, redraws rest of map) (Party A chooses 1 district, redraws map except all the "kept" districts) ... the maximum badness is minimal. Zeph Landau wrote, as best I can tell, only papers that haven't gotten a lot of traction on it and it needs more review. In the computational era, it doesn't take that long to alternate (or just give an hour to make each decision to minimize opportunity for taking advantage).

There are plenty of solutions that take the form of making individual districts more proportional, which I also like. If my section of rural Missouri elected 3-5 people with a proportional mechanism (or weighted voting privileges) then representatives would still be accountable to a local population, but the 40% population who identifies as democrats wouldn't be electorally meaningless, and vice versa in the city.
posted by a robot made out of meat at 6:09 AM on March 30, 2019 [3 favorites]

I bet this analysis would've been more broadly convincing to the judges if the mathematicians had included examples where the Democrats were doing the gerrymandering

You're hard pressed to find an example of a pro-Democrat gerrymander. Maryland is probably the best bet, and indeed was chosen as one of the new cases the Supreme Court heard this year. Most people assume as a way to get "both sides do it" in as part of the court discussion.

But it's not an accident that most of the gerrymandering in the US favors the Republicans. Where we are today is because of a deliberate Republican political strategy called REDMAP. A small group of Republican strategists invested $30M in winning various state races that would then let them control the 2010 districting maps drawn in those states. It's estimated this strategy netted them about 20 Congresspeople in the last decade. And it was all quite explicit and overt, they talk about it quite freely in the book Ratf**ked.

The Democrats didn't have a counter to REDMAP in 2010. But if the courts don't rein in gerrymandering it's only going to be worse in 2020, and maybe both sides this time. Both Republicans and Democrats are raising a lot more money to focus on districting. And the computer tools and data that enable gerrymandering have only gotten a whole lot better. As I mentioned above I'm particularly worried about what machine learning techniques can do. I think it will be a lot easier not only to build gerrymandered districts but clandestine ones, maps that look fair by the measures we're discussing here but will still have an engineered political bias that's hard to spot until it takes effect.
posted by Nelson at 7:01 AM on March 30, 2019 [6 favorites]

The problem is simple to solve but not easy, kick the repugs to the curb, and gently suggest that the majority of conservative's on the Supreme Court find other interests.


Oh look, I made it through a whole comment without once suggesting we burn it all down!



On review, sorry...
posted by evilDoug at 9:01 AM on March 30, 2019

A virtual district method could elect candidates based on statewide results and remove the local hazards of redistricting, fraud and winner-take-all. It would field candidates in the allotted number of districts, paired to district-specific opponents, then let anyone cast a single vote for anyone in the state. Each candidate would be seated according to the most votes in their virtual district, wherever the votes came from (accidental multiple votes will default to last choice). Bottom line is that the results will be skewed along ideological, racial, or gender lines, with parties strategizing the pairings, essentially conceding districts. It will thus prod them to diversify to capture votes beyond party lines. Cloned candidates in multiple districts will suffer the most because there is no gerrymandering mechanism to best distribute their votes.

Having said that, if the goal is to make concrete districts, then the most democratic way is to make incremental divisions chosen by those affected by the boundary at each division, like a reverse cellular automata. A state is first cut in half, then those halves are divided again, and so on. Everyone gets an increasingly weighted vote in all gradual border lines that affect their district. A bonus would be to limit both senators to half a state each.
posted by Brian B. at 11:26 AM on March 30, 2019

Moon Duchin is a colleague of mine—truly a wonderful person.
posted by haiku warrior at 1:39 PM on March 30, 2019

> Districts should be mathematically calculated to have the same population with minimum boundary length FULL STOP

Yeah, we have this discussion every time this issue comes up. The problem is NOT that districts are funny-looking. The problem is that the vote of many, many people is essentially meaningless.

Or to put it another way, the districts are unfair.

We pay far, far too much attention to making sure voting is fair for geography in this country--eg, 2 senate districts per state, electoral college, etc. The end-outcome of that type of think is essentially to give voting power to large tracts of empty land (ie, Wyoming, Nevada, etc). Wyoming, Nevada, etc, absolutely should get their fair share of electoral power based on their population, but absolutely not based on the fact that they happen to have many large tracts of nearly vacant land.

But democracy and voting are not about geographical areas or shapes--they are about PEOPLE.

Whatever method you use to decide districts has to focus on primarily on people, not primarily on shapes, geographical placement, and all those secondary things.

Part of the problem is that the very name "gerrymandering" focuses our attention on the odd shapes of the districts. But that is (at most) a symptom, not the problem.
posted by flug at 2:16 PM on March 30, 2019 [2 favorites]

Apropos of this topic is this talk (SLYT) from Mira Bernstein at Tufts on the difficulty. Specifically, shattering the "shortest boundary" idea.
posted by petrilli at 2:22 PM on April 1, 2019

The horror at proportional representation in the Justice's questions and the reassurance that none of this will create anything like proportional representation is... interesting. They go to pains to point out that if the votes of the party with less support are spread evenly throughout the population, that party will never get any seats no matter how much you re-draw boundaries.

This seems like it would have its most interesting implications in a state where the average political preferences of men and women are drifting apart but their living quarters aren't.
posted by clawsoon at 3:13 PM on April 1, 2019

I'm not a lawyer, but it seems to me that at least in some states, like NC, it would have made more sense to challenge partisan gerrymandering in the state courts under the state constitution.
posted by gryftir at 9:20 PM on April 1, 2019