Political Geometry: The Mathematics of Redistricting | Moon Duchin || Radcliffe Institute


[MUSIC PLAYING] – Thank you. Wow, well, it’s an honor to
be here at Radcliffe this year and to interact with all
the other amazing fellows. And in fact, the thing that’s
the most painful about it is not being able
to do everything. So it’s wonderful and terrible
to be talking to you about elections today, right after
an election that’s going to take a while to understand. So let me plunge right in
and start with the preface. It’s November 7. What just happened? Part of the answer
is I don’t totally know yet what my
story will be in terms of how to think
about it, but I want to take a moment to highlight
some non-candidate outcomes that may have been
under the radar for you. There were many. I’m particularly excited
that here in Massachusetts by an emphatic margin we
upheld anti-discrimination laws for trans people. [APPLAUSE] Florida– complicated
in other ways– emphatically voted yes to
restore voting rights for most people with felony convictions. [APPLAUSE] Arkansas and Missouri
voted emphatically again to raise their minimum
wage substantially. Medicaid expansion in states
you might not expect it. And real modernization
of registration policies in Maryland and Nevada
and in Michigan. And redistricting reform
seems to have won everywhere it appeared. Although, Utah is particularly
slow to count its votes. So this brings me
to the topic that I want to talk about today. What’s going on in
US redistricting? How can we– how are
we making progress? What are the inroads in
understanding redistricting and how to do it better? OK, so I think what I’ll
do, what I’ll definitely do, is invert maybe the
usual logic of a talk. Usually, you start
with the overview, and then you give your
kind of detailed work. I’m going to go backwards and
start with the math problem and come to the
overview afterwards. So here we go. Here’s the redistricting,
seen through the lens of mathematics. So the power the power
that comes with the ability to draw the lines, that’s
what we want to understand. So let’s do the
very simplest model. So in this picture,
you see five districts. And I’ve drawn in
the 50/50 line. And let’s suppose that
a state is made up of two kinds of voters, pink
voters and orange voters. And what we’d like
to do is understand if we have complete
omniscience and omnipotence, and we can put those voters
into districts, if we can just sort them out at will,
with only the rule that there should be an
equal number of voters in each district,
what can we do? Well, it turns out we can do an
extraordinary amount in terms of controlling the outcome. Orange can get no representation
with 40% of the vote, or it can get 80% of
the representation. So here are two pictures
that illustrate that. So there is the same kind
of volume of orange vote, 40%, in both pictures, or
maybe 40% plus epsilon. And you can see that, on
the left, because orange has 40% of every district,
orange gets no representation. Is the schematic clear? OK, and on the other
hand, if orange is able to arrange matters
extremely efficiently, then that 40% can be converted into
four seats out of five or 80% of the representation. OK, so at the outset we– you know, at first
blush, we should be kind of in awe of how
much control you have when you get to
organize the lines. But maybe this seems like a
vastly oversimplified model because, in fact, you don’t get
to pick people up and put them in buckets that the
districts represent. Instead, there’s geography. There’s demography. There’s all kinds of
complications and rules that delimit the problem. And I’ll come to that, but
let’s stay simple for a moment. So the way that you can get
such an extreme advantage is with two kind of
venerated strategies called packing and cracking. And what those mean is this. Packing is when you take the
power to draw the lines– in this case, orange has the
power to draw the lines– and you take the
other side, here pink, and stuff them into a few
districts with wastefully high vote totals and
then disperse them over the remaining districts. So packing is
overstuffed districts. And cracking is when
you have substantial, what some have
called wasted votes, because there are a lot
of votes being cast, but they’re not being
converted to representation. They’re dispersed. All right, and in
the other picture, it’s orange that’s been cracked. Right? So these are kind of the
hallmarks of strategies to extract extra
advantage from the ability to control the lines. OK, the next thing to note
is that the outcome doesn’t tell you everything
about what it’s like to live and vote
in a society that’s structured this way. So here are two
different ways of getting proportional
representation for orange– two seats out of five or
40% of the representation. But in one world, it’s a little
bit more randomly aggregated. And in the other
world, you live only with people who vote like you. Right? And it’s an open
question which is sort of a healthier
democratic state of affairs, but we can look
at how tendencies have been trending in the US
and think about what that means. OK, next point to
make, we have thought– it’s been a kind of idea
that’s as old as the word gerrymander, which
I’ll return to, that bad shapes, that
eccentrically shaped districts are really telling us that
something nefarious is going. Some agenda is being advanced. And I actually want to speak
against that narrative, somewhat, because
what I want to argue is that, if you
see the shapes, you don’t know the story that
they’re telling unless you see what’s underneath. Right? And so it’s not the shapes
of the district themselves. It’s how they slice up
the people that tells us how the outcome turns out
and that ultimately tells us about the quality of
the districting plan. OK, so let’s look at some
of the math up close, and we’ll start with
a very toy example. Instead of a big
complicated city or state, suppose I want to redistrict
just a 4 x 4 grid. So what you see here is
all 22 ways to do that. Right? So in each of these pictures,
I’ve taken a 4 x 4 grid, and I’ve cut it
into four districts. I’ve sort of Tetris decomposed,
right, the 4 x 4 grid. So they’re 22 ways to do that. But that’s up to symmetry. If I take some of these, and
I rotate them and flip them, I get 117 different
ways to do so. And that’s it. That’s all there are. But that’s already a
fairly complicated world to navigate if you’re trying
to understand the possibility space of districting plans. And it rapidly gets out of hand. Here’s the actual current
state of knowledge, which is fairly
appalling, when it comes to the combinatorics
or the number of ways to redistrict even
these small grids. So here’s what you’re
seeing in this picture. That 4 x 4 grid being
districted into 117 ways is shown here because those
were equal sized districtings. And by getting multiple
different algorithms at work on some of the fastest
computers available, this is how far we’ve
been able to get. So the numbers rise
fairly rapidly. By the time you want to
redistrict a 9 x 9 grid, there are 700 trillion
ways to do it. I would tell you how many
ways there are to do a 10 by 10 grid, but
that calculation has been running on the
OpenStack machines at MIT for over a month
without terminating. So you know, the
sea of ignorance here is pretty startling. But of course, states are
unimaginably bigger than this. So the problem is
that, if you want to understand the landscape
of ways to do redistricting, I would say that one
of the challenges, historically, in
approaching redistricting is that that
possibility space is way too large to think about. So let’s say you want to
redistrict Pennsylvania. You have its census blocks,
and you want to break them up into 18 districts. How many ways to do that? Well, if you started
to enumerate this at 1 microsecond
per plan, it would take until after the heat
death of the universe to get to your response. You’re just not going to do it. This is outside the
realm of what is doable. The good news is– and here’s
a little piece of magic. You heard a bit from Meredith
about my dissertation, which it’s true was
about Teichmuller space. In fact, what I did in
my dissertation was study random walks on a space of
surfaces, a 6, 12, 18, 24, 30-dimensional
space of surfaces. And the question was, if
you start to modify things randomly, and you do that
for a long time, what are the long-term trends. Well, in what feels to
me like a piece of magic, that same kind of
mathematics comes to bear on the
redistricting problem. So here’s what we’ll do. We can’t build out the whole
space of possible districting plans, but we can study it. We can sample it at random. We can do random walks
in the space of plans. So that’s what I
want to show you. OK, so I want to walk
around in this space that I can’t fully see. So I have to start somewhere. First, I need a way to
make an initial plan. So there are lots of ways
to do this, but one of them was, until recently,
displayed in the art gallery over in Byerly. You can take a
spanning tree approach and just form a spanning tree
at random, whatever that is– I’ll show you pictures of
one a little bit later– and then split off districts
of about equal size from it. And you get these bewitching
beautiful neutral districting plans. Under the hood, there are
fun computing algorithms for doing this for, building
these spanning trees. And they have great properties. There’s something called
Wilson’s algorithm that can sample uniformly from
the space of spanning trees and do it really fast. And here’s a kind
of image of how, if you color code
the individual steps, how you’re winding
around a space like this. OK, so we’ve got
some way of starting with districting plans. And then here’s the protocol. Just start modifying
them at random. You apply some kind
of proposal that tells you how to transform
one plan to a different plan. And what you’re
effectively doing is walking around the
space of possibilities. OK, so that’s what you see
happening in this picture. It’s computationally very light. This is a capture of
an in-browser demo. Your computer can
do this randomly. It’s extremely light computing. But it turns out that one of
the research innovations that has come out of our group
in the last few weeks has been a much more efficient
way to do it than this. So here again, I’m going to
use this term spanning tree. And let me show you the
picture of how to do it. At the side, you
see the process. On top, I start with two
districts, the orange and teal. And I’m going to do a move
I call a recombination. And that’s by
analogy with biology, all right, where you’re
taking some things and glomming them together
splitting them back up. And that’s like what
we’re going to do here. So we start with
these two districts. We merge them. We draw this random
spanning tree. So that’s a network with no
cycles that visits every node. And then I look one by
one at the edges of that. And I ask, if I cut
this edge, will I get pieces of equal size. If there’s no way to do that,
I pick a new tree and proceed. So all of this can be
done efficiently, quickly, at random. And then I cut at
a balanced place, and I get a new
pair of districts. Does that make any sense? Good, so let’s
see how they work. I’m going to illustrate this. Here’s of course Pennsylvania. And here are two
grids where I just want to show you the dynamical
system of these random walks and what it looks like. So I’ve started
the process on top. And in both of them, I began
with an initial splitting into these column districts. Everybody with me? And then we’re mutating
the districts flip by flip. And what I want you
to think about here is blind exploration
of an unseen space. You’ve dropped down,
and you’ve started making moves at random
without knowing much about the landscape. All right? OK, as I talk, I’m
letting this run, and you see it
really is changing, but it hasn’t forgotten
that it used to be columns. Do you see that? It’s got the memory
of its initial seed. I was giving it a
big head start so that I could try to impress you
with the efficacy of this walk. So this is this new
recombination move. It locomotes much
more efficiently around the space
of possibilities. And we have really good evidence
that, after just a short amount of time, it can sample
representatively from this unthinkably big space. That’s big progress, and
I’m scientifically very excited about it. And here it is on Pennsylvania. So this is a recombination
random walk of Pennsylvania. OK, and that’s a little
bit of the mathematics that goes into this. I’ll say there are some– you know, in another piece of
beautiful, magical synergy, it’s not only that the kind
of math that I know and love has something to say
about this problem, but the problem gives back
by raising spectacularly interesting new math questions. All right, so if you want
to understand this walk, it raises all kinds
of great questions about how spanning trees work. the probability that
there is a balanced cut of a spanning tree? Can you characterize this
Markov chain or random walk on the space of spanning trees? Lots of great questions,
open questions– this is kind of a research frontier
of this particular application. That’s the math model. Now let’s talk about
how it gets used, and then I want to zoom out
to the big picture again. OK, so as you heard, I was
very privileged recently to be asked to put this
in action in Pennsylvania. This press release
made me smile. So this is Governor
Tom Wolfe who was just re-elected comfortably
yesterday in Pennsylvania. And I think he
just really wanted to say “enlist non-partisan
mathematician.” What could sound more
objective than a mathematician? [LAUGHTER] But here was the problem. In Pennsylvania, it’s one of
the states with split control. It’s been a Republican
controlled legislature for some time. It has a Democratic
governor, as you heard. But they have to
agree on new maps. The state Supreme
Court ultimately was asked to
arbitrate a case that invalidated the plan
that was enacted in 2011 as a partisan gerrymander. And that’s the
plan you see here. It’s a fairly notorious plan. It’s districts look
pretty disgusting. I like to characterize
shapes like this as tumors and fractals. It’s got this
notorious district here in the suburbs of Philadelphia. Some people call it Goofy
kicking Donald Duck. All right, I’ll show you a
close up a little bit later. And it was thrown
out by the courts. And then the task of the
legislature and the governor was to agree on new maps. And what you see here is three
different attempts at new maps. And other than tumors
and fractals over there, I would say that, to my
eyes, the other three look qualitatively fairly similar. I don’t think their visual
tells of nefarious intent in any one more than the others. Yet they perform
very differently. So that’s the task here
is to use that math model that I
described to do kind of forensics on these maps. As it turns out– so that was the 2011 plan. This was the new plan
floated by the legislature. Interestingly, they
didn’t pass it as a bill. They floated it on
Twitter, true story. [LAUGHTER] This is the plan that
was counter proposed by the governor’s team. I want to emphasize that
that was not my job. I was doing map analysis,
not map creation. So this was one of the
maps that I analyzed. And this was the plan
that was ultimately enacted by the courts. OK, so the challenge is to
understand what they’re doing. OK, before I get
back to that, let me talk about some
research findings that are enabled by this math model. And one of them I’ll try
to illustrate on our home state of Massachusetts. And the finding is you don’t
get proportionality for free. Before I explain this
picture, let me just say out loud what I mean. In Pennsylvania, it has
been the case for some time that the partisan voting
patterns are about 50/50, Democratic and Republican. But with about 50% of
the vote, Republicans had been getting 13 out of
18 seats in the Congress, in the congressional delegation. And some people took that to be
prima facie evidence of abuse. How can you be converting
half of the votes into 72% of the seats? Right? So one of the
findings of the model is that you’d be surprised at
what happens when you neutrally redistrict. You shouldn’t expect
proportional outcomes to just come for free. And actually, one of the punch
lines of this whole research enterprise and of
the talk I hope is proportionality
is complicated. If that’s what
we’re after, we have a bad system for securing it. And there are others. I’ll come back to that. OK, but I wanted to illustrate
that with Massachusetts because here’s a fairly
dramatic example. So what you see
in this picture is an image that comes
from voting patterns in an actual election– Kennedy versus Chase
for US Senate in 2006. This election was an
interesting geometry. What you see in the picture is. This chase got over 30% of
the vote in that election. Now, of course, that
was a Senate race. But now let’s just imagine that,
with people voting that way, let’s imagine that
I tried to district some into nine districts. Massachusetts currently
has nine districts. How many seats
would you expect– in how many districts would
you expect a Chase majority? Well, you might think,
since this is about a third of the vote, I’d expect Chase to
get up to a third of the seats or maybe more, right, maybe two
or three out of the nine seats. Right? What I’ve done
here is highlighted the most Chase-favoring possible
collection of precincts. And I’ve just aggregated
them until I get up to the size of a
congressional district. So that’s a ninth of
Massachusetts’ population. Everybody understand
what I’m highlighting? OK, so Chase we
think maybe should get two or three districts. This would be the first one, the
most Chase-favoring district. Yet this collection
still prefers Kennedy. OK, so I hope there’s a
little surprise there. And let me try to reiterate. Here it is. There are more plans for how
to district Massachusetts than particles in the
galaxy, literally. Yet every single one of them
has a 9-0 Democratic delegation, every one. Right? So if you thought, based on the
intuition that proportionality is natural or
desirable, maybe you would have thought that
Democrats are gerrymandering Massachusetts. Right? They’re locking out Republicans. But it’s should the
math that’s locking out Republicans in Massachusetts. So even if I let a
district be scattered and discontiguous
like this, I just couldn’t get Republican
representation here. OK, phenomena like this are
interesting in every state. You see where the
votes are, and then you have to see how districting
handles those votes. And the answer isn’t
always what you expect. OK, second finding, shape
signifies less than you think. Here are two plans
of Pennsylvania. And what I’m going to do
is use a common metric from political science
called the mean-median gap to see if these plans are
built to favor Democrats or Republicans. And here’s what we get. So we ran this Markov chain for,
in this case, a billion steps, a billion steps of
the Markov chain. And here’s the plan that
was enacted in 2011. And that’s a billion
plans similar to it. And what’s being
measured here is how much the plan
has a partisan skew in the Republican direction. So that’s the
Republican-favoring direction. And what you see is that
the current plan is here. A billion similar
plans are here. That plan is not
just an outlier. It’s not just in the thin
part of the bell curve. It’s in what I like to call the
invisible part of the curve. OK, here’s the new
plan that was proposed by Republican legislators
earlier this year. It’s called TS, the
Turzai-Scarnati plan. It looks just fine. But under the hood, it
performs strikingly similarly. There’s the plan. There’s the billion
comparison maps, invisible part of the curve. OK, even though
there are surprises when you do analysis
like this, it does still actually vary
in whether it tells you that a plan is an outlier. So here’s the plan of
the governor’s team, which, again, I
wasn’t a part of made. In fact, not only
was I not part of it, I was in some suspense
about how this test would evaluate this plan. And here’s the answer. Not every plan is an outlier. Some plans sort of hit the
meaty part of their distribution of comparisons. All right, does that make sense? OK, so what’s going on here? We’re learning that
a test like this can tell you when a
plan is very extreme or when it shares properties
with most other things or many other things in this
universe of alternatives. The way this is intended to be
used is not to select a plan. It’s to rule out the ones that
are most egregiously outlying. OK, so that’s the math model
and an application of it. And now what I
want to do is kind of look at the stakes,
which we haven’t really talked about yet. So before we can
get to the stakes, we have to say something
about the realistic rules. So what are the rules
for redistricting? Well, plans must be
population balanced. I’m going to quickly review
some of the common rules. Actually, before I
do this, I should say the states have a lot of
authority and a lot of latitude in how they make
their own rules. Very few of them are universal. But here, this one is. It’s almost the
only guidance that’s extracted from the Constitution. And it says that the plans
should balance population. For legislative districts,
they need to balance typically to within 10%. For congressional districts,
the current practice, believe it or not, is
to balance the census population of your districts
down to one person deviation. OK, so that’s
insanely stringent. Two, compact, so this
is a vague desideratum. And it says that the district
should have a reasonable shape. And that’s activating
that intuition that bad shapes are
red flags of nefarity. We see again Goofy
kicking Donald Duck, maybe kind of flouting that
compactness a little bit. The next requirement is
that the district should be connected in a single piece. This is, but just. So there’s actually two
different cut points in this district, two different
places where the district could be disconnected by the
removal of a single building, true story, a hospital
and a seafood restaurant. OK, next, the districting
should avoid splitting counties or cities. Here’s a picture to
illustrate that that’s hard. This is Columbus,
Ohio and its county. And they actually overlap
each other in an odd ways. So if you’re a
redistricter, and you try not to split that
county and that city, that’s actually
complicated guidance. Avoid splitting
communities of interest. This is a very interesting
rule and a very slippery rule and a very lightly
enforced rule that says that, when you have
a community with a shared interest, you should try
to keep them together. And then, finally and
crucially, there’s the federal Voting
Rights Act of 1965 that discusses opportunity
for minority groups to elect candidates of choice. And I’ll come back to that. I put this slide up as a
reminder of the humility with which you have to approach
this problem as a modeler. Right, these rules are
difficult to operationalize. They’re difficult to prioritize. They’re difficult to
incorporate into your model. And yet, they’re essential. So sometimes, you’ll see
modelers ignore the rules that they can’t quantify. And that seems to me to
be modeling malpractice. OK, so I think, when you want
to make an applicable model, you want to think
really hard about how all your rules interact. OK, so what are the stakes? Here’s an image that
shows you something about US redistricting. So this shows you about a
dozen different districts around the country, face blends
of their average district resident, a home at the actual
median price in each district, a recent ballot initiative, and
the representative downstream from all of that. And when you look at
the texture of this, you really start to see
the delicate dependence on line drawing for vastly
different representational outcomes. So let’s take a look
at Southern California. So here are California 43
and 49, two districts very close to each other in
Southern California. Because of how the
lines are drawn, they have quite different
district residences in terms of the demographic
makeups of their districts, vastly different median home
values and per capita incomes, in the case of 43, a median
home value that’s many, many times its
per capita income. They vote differently on
California’s myriad ballot initiatives. And they get very
different representation. So this is from the last cycle. And many of you may recognize
the inimitable Maxine Waters and the also
inimitable Darrell Issa. And this leads us
back to this point. Here those two districts
again on a map of the country. They’re tiny, and they’re
delicately constructed. And it may give you a
whole lot of bewilderment about exactly everything
that flows out, but it’s a reminder of the
stakes of this line drawing process. OK, so under the hood a little
more, let’s look at Ohio. Here’s how Ohio voted in 2016. They had just over half the
votes went to Republicans in the congressional
race, but 3/4 of the seats were to Republicans in
the congressional race. This is a model that
tries to understand what would happen if you model
partisan swing towards one party or the other. So if you take the vote in
the different districts, and you dial it
gently up or down, this is how it would vary. So what’s the
conclusion of this? The conclusion is that that
12-to-4 delegation would have occurred– you see this
giant plateau here– with Republicans getting
anywhere from 49% to 79% of the vote. Is this wildly effective
gerrymandering or an artifact of where people live? That’s what the math
model can do for you. Meanwhile, here are the stakes. OK, these are the 16
representatives of Ohio before yesterday. And now I’ll show you the
16 representatives of Ohio after yesterday. Here they are again. OK, there wasn’t
really a close race. By contrast, Pennsylvania,
which had its lines radically redrawn in the process
from earlier this year, had enormous makeover of its
congressional delegation. Interestingly, Pennsylvania’s
18-person delegation was the largest in the country
to be all-male until yesterday and elected four women
for the first time. I think it’s the year of the
blonde woman in particular in Pennsylvania. OK, so the stakes
of all the math are actual representatives
who go to Washington and behave quite differently. So I want to devote this
next section of the talk to kind of revisiting
the redistricting problem as a nexus of
concerns from many different disciplinary traditions and
for many different fields. OK, history matters
for understanding how redistricting works. So as many of you
probably recognize, here is the original
gerrymander. So here we are. This is a picture from
the North Shore of Boston. And it’s a districting
plan that was approved in 1812 by then
governor Elbridge Gerry. Some of you may notice,
as you tool around town, around Cambridge,
how many things are named after him around town. So there’s Gerrys
Landing Road down when you’re trying to get from Mem
Drive from around the corner onto Soldiers Field. There’s Gerry Lane right
up four blocks from here. Who was he? Besides the governor
of Massachusetts, he was sort of one of the
giants, the so so-called founding fathers. He was a representative. He was a, well,
governor until 1812. He actually was voted
out in this election and then became Vice President. So he sort of has
his fingerprints all over really America. What’s going on in this picture
is a congressional district that was thought to favor
Gerry’s Democratic-Republican Party over the
rival Federalists. For those of you who’ve had the
pleasure of seeing Hamilton, which I recently
did, you got to see these two rival factions,
in the persons of Hamilton and Jefferson, battle it out. Here’s the political cartoon– this one’s from 1813 in the
Salem Gazette– that kind of brought that to life. And I want to actually show
you a little bit of its text because I think
it’s fascinating. “Federalists, followers
of Washington, again behold and shudder
at the exhibition of this terrific
dragon brought forth to swallow and devour your
liberties and equal rights. Unholy party spirit and
inordinate love of power gave it birth. Your patriotism and
hatred of tyranny must by one vigorous struggle
strangle it in its infancy.” A little over the top, perhaps. What’s the argument
that it’s making? It’s that, from its
shape, as exaggerated here by its claws and its
wings, Gerry’s salamander, or the gerrymander,
is giving you evidence of its unfair and bad design. So that’s kind of the partisan
terrain in gerrymandering has been fought out
since at least 1812. But the 20th century gives
us a different history of gerrymandering. So here’s the
gerrymander of the 1950s. What we see here is
Tuskegee, Alabama, which redrew its own
city lines in 1957. So that made its way–
that was challenged and made its way
up to the Supreme Court in a landmark case from
1960, Gomillion v. Lightfoot. So before the redrawing,
Tuskegee was larger. It voluntarily shrank itself. It used to be the green
square that you see here and then redrew itself to be
this 28-sided eccentric looking polygon. Why? You won’t be surprised to
hear before the redrawing Tuskegee was nearly 80% black,
and then it became actually 100% white after the redrawing. So there’s such
pervasive and dramatic residential racial
housing segregation that it’s possible
with surgical precision to draw yourself
a one-race city. This particular case was fairly
easy for the Supreme Court to handle because it’s a
matter of disenfranchisement. If black voters here are
drawn out of the city, they’re in unincorporated
territory in Alabama. They have no more mayor,
city council, city services. They’ve lost a vote. So the Supreme Court
threw this out. This was fairly easy. The congressional
case is a lot harder because, when you’re drawn out
of one congressional district, you’ve drawn into another. So it becomes a matter
of weight of votes and not of having or
not having the vote. And to this moment, the court
has kind of continued to punt. The Supreme Court has continued
to punt on how to handle that. OK, onward into
the 1960s, here’s a picture of Mississippi. Now the black population
in Mississippi is concentrated here
in the delta region, and Jackson is around there. Here are some districting
plans of Mississippi before the 1960 census. And here are the three
plans that the Mississippi legislature considered
after that census. Look what’s happening. Whereas the delta used to be
preserved in a single district, it’s split two or three ways
in each of the new plans, guaranteeing zero
majority black districts. So this is the
fundamental context of all of the legal
framework that we have around gerrymandering today. So it’s the civil
rights moment that gives birth to the biggest tool
that we have for voting rights. And that’s the Voting
Rights Act of 1965. Here’s an image from
the signing ceremony. So this is a powerful bill
that was originally aimed at eliminating so-called devices
blocking the black vote– poll taxes, literacy
tests, and so on. Some historical hot spot
regions around the country were bound by Section 5
of the Voting Rights Act to request preclearance
from the federal government before they could make any
changes to their voting rules. Actually, I want to emphasize
how important this is. This isn’t just you need
prior permission if you want to change the districts. It’s all changes to your
voting related rules– early voting hours, polling
locations, all of that. You need prior approval
from the federal government. In 2013, that was swept away in
a Supreme Court decision called Shelby v. Holder. What that’s left in
its wake is a situation where multiple states had
restrictive new voting laws cued up and ready
to go for this decision. Three or more states passed
new voting restrictions the day this decision came down. And now, instead of
being blocked in advance, those have to be
litigated after the fact. All right, so it’s changed
the landscape considerably. But the Voting
Rights Act for now lives on and is still
a very powerful tool. It’s been frequently renewed
and expanded in interesting ways that I won’t get into. That’s the subject of
a whole other story. But it’s still on the books. It’s still important. And it’s still, in some ways,
the only legal tool that we. Next, a reminder of all the
ways that this matters– so here we are in Massachusetts
where we currently have nine congressional
districts, but we have all kinds of
other lines and zones. We have a state
Senate with districts, a state house with districts,
a governor’s council. We have school districts. And here in Boston,
I think that should have a specially resonant
history because, in the 1970s, it was specifically not
just the idea of busing, but how that busing
was implemented in terms of zones,
maps, and who would be bused where, that
triggered racist riots and gave Boston a long enduring
reputation as a racially problematic city
among many others. Interestingly, when legislators
can’t agree on a map, courts throw it to
an outside expert. That expert is called, in
a fairly resonant term, a special master. So it was a special master who
drew the school busing map here in Boston that cross-bused
between Charlestown and Dorchester, particularly,
some say igniting the powder keg that became the riots. And it’s a special master who
redrew Pennsylvania’s map. It’s a special master
who’s been called on to redraw Virginia’s map. So this is still very much
a system that’s in effect. This slide is also
intended to remind us, in terms of the
history and the stakes, that it’s not just Congress,
but redistricting also has a very local texture. And where the rules are
more constrained when it comes to
congressional districts, they can be much
more up for grabs when it comes to
everything local. OK, these narratives intertwine. So I’m going to end this
talk with just four vignettes about the power of these
kinds of forensic techniques to show us how
redistricting works around the country in
a way that combines these various elements. Notorious district,
Illinois 4, the earmuffs– anyone recognize it? OK, those of you from Chicago
may recognize it better now. Here it is sitting
inside the city, connecting Pilsen, a
predominantly Mexican neighborhood on the south
side, with Humboldt Park, which is the center of the city’s
Puerto Rican community on the north side, strung
together via a highway. What effects does
the construction of a district like this have? Packing. So Luis Gutierrez did
represent this district– he’s decided to move on– but from 1992 continuously
to 2016, never getting less than 75% of the vote. OK, so this looks
like a textbook case where Latinos have been
packed in inefficient numbers into a district to dilute
their voting strength. But in an interesting
twist, this turns out to be friendly
packing, endorsed and actually aided by civil rights groups. An actual image for you
from John Oliver’s show of a real-life wedding cake
of two redistricting legal experts– “Nick Ruth, Combining
Communities of Interest”– because they both
worked on this district. So what’s the story
of the district? It’s a Latino district
that was built to interlock with three
African-American districts also locking in and heading
towards the south side. What I find
fascinating about this is that it’s a well-meaning
gerrymander in a sense. It’s predicated on the
idea that, in order to comply with the
Voting Rights Act, you want separate
opportunity districts for different racial groups. I’m happy to say
that today, in 2018, we’re starting to see
some of that logic break down, as civil
rights organizations, like the Lawyers’
Committee and others, are bringing for the first time
coalition voting rights claims. So right here in Massachusetts,
the Lawyers’ Committee has a case in Lowell,
which is a coalition Latino-Cambodian
voting rights claim. OK, and I think this is a
new and important frontier in the history of
voting rights litigation where, instead of creating
separate and kind of calcified, ossified racial categories
with separate districts, there’s more coalitional
thinking going forward. Ironies of segregation–
here’s an image that comes from a white paper
that our research group put together because we were
asked to look at redistricting in Santa Clara, California. Before I tell you what’s
happening in the picture, let me give you a bit of
back story on Santa Clara. It’s about 40% Asian and was
sued by Asian civil rights groups because its six-member
city council had never had an Asian member, OK,
with a 40% Asian population in the city the city, interestingly,
said you’re right. Our system is
terrible and racist. Let’s replace it. And OK, they didn’t
in those words. And the interesting contestation
became replace it with what. OK, so we used our models to try
to understand how districting would work because that’s the
go-to remedy when you throw out an at-large city council
system is to move to districts. And here’s an irony
that we found. So in this simple
model, I’m showing you 40% of the population either
scattered in a regular pattern, semi-clustered, or clustered
as in a kind of more segregated way around the city. Then we run our model. The computers go boop,
boop, boop, boop. And they tell us what kind
of representational outcomes we should expect. And what we found
surprised me quite a bit. What we found was this
is not surprising. If you’re very
checkerboarded around a city, you’re not going to do
very well under districts because you’ll have a
minority of every district. Does that make sense? That should be kind of obvious. On the other hand,
segregation does at least ensure a strong possibility
of representation. But here’s the surprise. As you kind of interpolate
between these extremes, it takes a long time for your
representation to kick in. So here’s our kind of
semi-clustered configuration. And check it out. It performs just as
badly under districting as the checkerboard. So from a mathematical
point of view, there’s a kind of
phase transition that occurs as you cluster more. And representation
doesn’t kick in until you’re fairly segregated. So I call this ironies
of segregation. Just a few more images, this
is ongoing work modeling the situation happening
right now in Virginia. So here are three
maps of Virginia in the wake of
its district court throwing out its house
of delegates’ plan as a racial gerrymander. This is the enacted Republican
plan, a democratic counter proposal, and an independent
third party group. And what we were able to do
is, using our ensemble methods, building big piles
of comparison plans, we can see how each of these
performs in the distribution of black voting age population
compared to neutrally computer generated maps. And what you see is here’s
a zone of black population where you’re empirically
likely to be able to elect a black representative. And I hope this gives you
kind of a forensic glimpse into the statistical
guts of these plans. It’s showing you that, for
instance, this Republican plan elevated or packed black
population in these districts so much that it’s depressed
in the next batch or two of districts,
costing opportunity for African-Americans to
elect candidates of choice. But the analysis shows you more. Here’s the zone where
you’re more likely to elect white Democrats. And that’s where a
lot of blue dots fall. OK, so an analysis
like this can show you whether districts are geared
towards black representation or, perhaps, maybe optimized
to elect more white Democrats. Finally, let’s come full
circle to Mississippi. And I’ll just say, with our
methods of generating plans, we were able to
generate millions of alternative Mississippis. Today, Mississippi has four
congressional districts. One of them is about 2/3
black, and the others are 1/3 black or less. It elects one black Democrat
and three white Republicans. And what you see,
as you randomly explore that vast
space of possibilities, is that it doesn’t
need to be so. And Mississippi could
have a vastly different congressional delegation and
a vastly different balance in its districts, and it takes
computers really just a second to find other ways to do so. OK, so I’ll close
with the punch lines. What are the bottom
lines about the lines? Small picture, the rules
interact in complicated ways, but the models can help
us figure that out. The eyeball test is dead. It no longer can tell us when
something’s been gerrymandered. Deviations from proportionality
are more complicated than we thought. And there’s maybe even a
new normative story here about gerrymandering. So what is this outlier
test bringing to us as a matter of fairness? It’s asking the
question, does a map behave as though drawn only
from the stated principles. And where it deviates,
is there a reason? These are the kinds of questions
that this outlier analysis can bring you. In the big picture,
I hope the takeaways are that single-member plurality
districts are a legacy. They’re an artifact of
many layered histories that I hope I’ve outlined. You can’t tell the
story of redistricting without the story of the
black vote in particular and the violent and genteel
efforts at suppressing it throughout US history. There’s a kind of
perverse irony in play that districts work best
to secure representation for a numerical minority in the
presence of marked segregation. And so less
segregated populations are much harder to represent
with a districting system. This is true not only for
Asians in Santa Clara, but for Republicans
in Massachusetts. All right, this is true
for any numerical minority. Republicans are just not
segregated enough here in Massachusetts. The Voting Rights Act
is a fundamental tool, best that we have, but it
calcifies racial categories. And then the math
model, what does it do? It gives us a baseline
for neutral redistricting. It reveals forensics
of map design. And it lets us
challenge our intuitions that something is being gamed. Fairness or justice does
not equal neutrality. And that’s another matter. And so computers should
never draw our maps for us. They should be tools that rein
in the most extreme abuses. Thank you. [MUSIC PLAYING] [APPLAUSE]




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