The Math Behind Gerrymandering, Fair Representation, and Politics with Karen Saxe

All right, so Karen, earlier in your career you worked on gerrymandering, which I think of as a political topic, but you're a math professor, so what does that have to do with math?

Yeah, great question.

So gerrymandering is actually the sort of messing about with what's really called redistricting.

Redistricting is the third step in this process that happens every 10 years, and all three are mathematical.

So there's the census that happens, and then the reapportionment of congressional seats, and then redistricting.

And then that's where gerrymandering comes in.

Every 10 years since 1790, we perform the census, and these n- uh, numbers are then used to, um, distribute the 400-- the now 435 House of Representative seats out to the states through reapportionment.

The census is required in the Constitution precisely for this reason of apportionment.

So those two things have happened every 10 years, um, except for one time in 1920, which I could talk about why if you want.

It didn't happen then, and people's guess is always wrong about why it didn't happen.

In any case, those things happen every 10 years.

And then, um, redistricting happened, but since 1842 it's been mandated in law that it has to happen.

And, um, that's to decide which, which people in the state, you know, said representative actually represents.

So cutting up the state into these geometric shapes.

And that brings me to what math has to do with it and what, you know, what I kind of worked on.

So when I was a-- I was trained in operator theory, and that's what I did my first mathematical work in, and I was studying, I know this just sounds so weird now in a way, but like, okay, the spectrum of an operator, which for people listening, if you don't know, the spectrum of a, an operator is the analog of the set of eigenvalues for a infinite dimensional operator.

And that's a set in the plane.

And I was studying sort of like how many holes that set could have, its convexity properties, and so on.

And the-- then I was, for some reason in around the early 2000s, I was reading about redistricting and measures of compactness.

So since like the 1960s, certain things have had to happen in redistricting to guard against gerrymandering.

You might be looking for does the shape look not natural? It-- does it have long arms? Does it have holes in it? And there's, there's rules about that and laws.

Some, some are laws, some are guidelines for states.

Now let me just ask here.

Yeah.

I'm guessing when political people, judges are talking about whether a district looks compact, they're not talking about infinite open covers having finite subcovers, right? [chuckles]