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So in this segment, we're going to be talking to Ben Blum-Smith,

who I'll have introduced himself,

about the math behind Gerrymandering.

Also, will be covering a little bit as well about the technology and

algorithms that support how it is that people approach the redistricting process.

So Ben, if you would, please introduce yourself.

I'm Ben Blum-Smith, I'm a mathematician.

My background is in pure mathematics,

but I got really interested in all the contact surface between math and

democracy when I found out that

mathematicians were doing really interesting new work in gerrymandering.

So, the last year

gotten follow up on that and I'm currently doing a head residency,

then I will be doing a Ted Talk in a few weeks on that.

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Great. So, I have a few questions for you actually.

So, the first of those is, we hear,

and especially when I'm going out to talk to audience about this,

the question, is gerrymandering really a math problem?

So, do you see gerrymandering as being a math problem?

So, let me hit that from several different angles.

If you are a legislator in control of and your party is in control of

the redistricting process and you just

really want it badly gerrymandering as much as you possibly can,

then that is a a math problem for you.

I mean, it's a real life statistics problems,

dirtier than a pure math problem.

But you've got whatever data you have about this state and where the voters are and

which way they vote and whatever predictions you can make about which way they vote

and as fine-grained detail as you have access to,

you have whatever technology you have where you can overlay that data onto a map.

Then you have like trying to find the math that best advantages

your party and that is essentially a mathematical optimization problem.

So, I do think that's a math problem.

If you are a citizen who doesn't like the idea that the legislature is doing,

then you have a problem that's a political problem and

a legal problem that maybe math can be of some aid to you in trying to solve.

So, that's how I see that as being an essentially,

I see also is having a political and legal problem that maybe math can help with.

Then, as far as the problem of actually drawing a good map,

a map that is intended to reflect the will of the people,

to me that's also essentially a political, legal,

and social problem that math maybe has something to say to.

Does that answer your question?

It does. So, as a follow-on to that,

assuming that there really are ways that you can use math to help as a tool.

So, does there exist an algorithm or a set of algorithms

that would help to make the process fair?

So, is there like an algorithm you could say,

"Hey, across the country,

let's use this algorithm and it will draw the lines for

us without all the bias that people bring to that process.".

The question is, let me just make sure I understand the question clearly.

I think that the question is,

can we farm out,

can we sub-contract the work of drawing good destructing maps to

a computer and thereby eliminate human bias and political malevolence?

Yes. It's a really good way of framing the problem, yes.

No.

There are a few things I have to say about that.

One is that a computer algorithm,

I'm going to quote my colleague Cathy O'Neil here who wrote a beautiful book

about the process of

humans tending to farm out our

social decision-making to computers and what that leads to a dozen.

Well, she said "An algorithm isn't opinion embedded in code."

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So, the thing is a computer program has to make decisions.

This is what I see, okay.

The person who wants the computer to solve the problem for us,

has in their mind the idea that there's a right answer to this question,

there's a correct map for this state.

The truth is that the number of possibilities for redistricting of a state,

exceeds the number of atoms in the universe.

There's just an immense space of possibility and inside that space of possibility,

some maps favor some interest and other maps favor other interests and there's not

a like platonic form of a pure only right map that we can try to find as a math problem.

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equal population between the districts,

respecting traditional political boundaries like County lines,

keeping together communities of interest.

In some states, protecting incumbents is seen

as illegitimate redistricting and then in other states,

protecting incumbents is seen as antithetical to legitimately district.

So there are some of these types of priorities that are contingent.

Then there's the Voting Rights Act.

The Voting Rights Act put certain obligations on states

to make sure that minority populations have

the ability to elect elected officials of

their choice if the rest of

the population is voting is blocking them out of the process otherwise.

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People want it to be that the districts look nice,

then everything that they desire out

of a district thing will be there like they will have their representation in

competitive districts and news some interest in tact and everything

but actually these things are in a fight lucha.

Even to the least controversial ones,

equal population and not splitting counts,

not splitting pre-existing political boundaries.

Even these two are in conflict.

In fact, when the Supreme Court

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One impact that I'm not going to speak on whether the broader implications of that,

but one impact of that was that it made it impossible to keep all counties intact.

So, because the equal population on was not needable with out

breaking up some towns and that weakened the norm of not splitting up counties.

So now, that created a room for map makers to maneuver,

it put one constraint on them but it created a different room.

It said you have to have equal population,

but you don't have to respect county boundaries.

I mean, you should but you're not going to be able to perfectly.

So how much is too much is a fuzzy area.

I was speaking with a legal scholar a few weeks ago and whose

opinion respecting county boundaries is more of a ties the hands of gerrymandering,

is more effectively than equal population does.

So to him, that was weakening of the protections against gerrymandering.

But the point of all of what I'm saying is

just this list of interests are not the same as each other.

So, making a map is trading off interests and it's that's cooked into

the fundamental project of what the problem is and

any algorithm that is programmed to draw a map is going to make certain choices,

just by the nature of the problem

about how those interests are going to be balanced against each other.

So it's not an objective thing, it just isn't.

So, shifting gears a little bit,

we've talked in this elsewhere and this teach out

about the efficiency gap with Professor Stephanopoulos.

What are some of the other strategies that we've historically used

to help to represent gerrymandering or help to detect gerrymandering?

Beautiful questions. So, these fall into

two broad categories that are very different from each other.

One is bad shapes.

Back to the original,

the word gerrymander comes from a map passed by

the Democratic Republican Party in early 19th century Massachusetts,

which was the party of Elbridge Gerry.

It was claimed that one of the districts

that was drawn by his party looked like a salamander.

So, Gerrymander a portment to of Elbridge Gerry's name with the word salamander.

The point that why I bring this up is because that had to do with shape.

People were like look at that ugly shape,

it looks like a monster.

There must be something wrong.

So, one way that we've tried to get a hold of gerrymandering is to say that,

and that's where the traditional compactness standard comes from.

So, one way we've tried to do is measure compactness,

and there are a couple of traditional ways based on classical math,

to say that a district is real long.

One is to say if the length of the perimeter is really,

really long compared to the area,

like a circle has the smallest possible perimeter given it's area, but if it's really,

really non-circular even it could have a really,

really long perimeter, without enclosing much area.

So, there's a measure of that called the Polsby-Popper score.

That's one whole train of thought.

The other train of thought is looking at the outcomes.

So, that's like wait a second,

there must be, I smell a rat.

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Often for example, in the reporting around

the Wisconsin state legislature map which is before the Supreme Court right now.

We'll probably see what they think inside of the next month.

You constantly see in the reporting that in 2012 election,

the Republican state legislators got a total of 48.6,

I think it was percent of the vote,

and yet they got 60 plus percent of the representation in Congress.

So, some kind of a measure based on looking at the result,

and thinking the result looks wrong.

The most naive measure of that kind is just the kind I just said like

comparing the total vote share to

the total seat chair as percentages and noticing a big gap.

The Supreme Court rejected that as a standard to detect gerrymandering in 80's.

This is sort of a sad fact of life for everybody for who's intuition that,

I think a lot of Americans have the intuition that's what it should be.

There should be a match between the votes and

the seats percentage wise of the two parties,

but you're not going to get that in the system we have.

We have this system where you have single districts represented by one congress person,

and the state legislators often work the same way where there's just a district,

and in that district the person.

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Somebody might suspect gerrymandering but,

it's actually very hard to draw district that

could consistently elect a Republican legislator in Massachusetts.

Because even though there are at least 30 percent of the state,

that votes consistently Republican in nationwide elections,

they're not geographically concentrated in the state.

So, that's just the point I'm making is just you can't expect in this system

we have where it's about geographic concentration,

who elect people right here,

you can't expect proportionality.

So, that was the first naive idea was like okay,

big gaps in the proportions means something is wrong.

The second sort of more nuanced way to approach

it is measures of what's called partisan symmetry,

and the efficiency gap is a sort of a measure of partisans symmetry and others.

For example, you can look at the mean,

median gap. Here's what that is.

You take all the districts in the state,

and you look at the percentage of the vote

that one of the parties got in each of those distance.

Like maybe in this district,

they got only 20 percent,

and in this district they got 25 percent,

in this district they got 50 percent,

in this district they got 85 percent.

You look at that sequence of numbers,

then you find the middle number.

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How could this be? Well, here's how.

This could be a sign that A was gerrymandered against.

Because what happens if A is gerrymandered against is that

the other party tries to concentrate

A's voting power into the smallest number of districts as possible,

and spread out the rest of A flowing power across the rest of the district,

so you can never have a majority in the rest of the districts.

So, that means that you get situations

where there's just a few districts that are like completely dominant party A,

and most of the districts are a little less than half for party A.

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So, what will happen is that the median number for party A will be

below 50 percent because only a few districts have above 50 percent for A,

most of the districts have below.

Maybe they like almost all of them have 45.

So, the middle one will have 45,

the numbers will be like 40,

44, 45, 45, 45, 47,

46, that was in the wrong order,

it's should be 46,47, and then like 80, 80, 80.

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So, in that case, the middle number is going to be around 45,

but that number doesn't reflect the actual voting strength of party A in the state,

because in the districts that they win,

they win in a landslide.

So, the average vote in the state is higher than that number.

So, that gap for exactly the reason I just described,

is seen as a measure of some kind of

unfairness in the distribution of the votes between the parties.

The idea captured by that mean,

median gap is that,

okay maybe it's not going to be proportional,

there's no reason for it to be proportional,

but it should be symmetric between the parties.

This is a concept that was offered by political scientists to try to

capture what fairness might mean in the context in the district area.

The idea is the plan should treat the two parties so that okay,

fine, your party can win 80 percent of the seats with only 53 percent of the vote.

But what if the mood in the state changed,

so that my party won 53 percent of the vote.

Will this plan also give it 80 percent of the seats? Did that make sense?

It did to me.

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The ideas, if there's a shifts.

Okay. One party has a lopsided advantage compared to its vote share under this plan,

but if there was a partisan shift in the partisan mood to the other party,

would they get the same lopsided effect?

If they do then that's the argument goes,

that some kind of fairness,

even if it isn't proportionality.

Those were the ways we had of measuring it up until pretty recently.

Right. Well, wonderful.

Thank you so much for those explanations,

they are very clear.

We hope that you will join us in the next segment as we

continue this discussion about redistricting reform and gerrymandering.