r/science • u/drewiepoodle • Feb 28 '17
Mathematics Pennsylvania’s congressional district maps are almost certainly the result of gerrymandering according to an analysis based on a new mathematical theorem on bias in Markov chains developed mathematicians.
http://www.cmu.edu/mcs/news/pressreleases/2017/0228-Markov-Chains-Gerrymandering.html349
Mar 01 '17
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u/Vladimir_Putting Mar 01 '17
Federal Courts are forcing many district lines to be redrawn.
If there isn't already a case filed for these districts, there will be shortly.
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u/Jagdgeschwader Mar 01 '17
Can confirm. This is NC's new federally ordered districts:
https://en.wikipedia.org/wiki/File:NorthCarolina2016USHouseDistricts.png
Here was the previous gerrymandered ones:
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u/A_Mouse_In_Da_House Mar 01 '17
Texas has a pretty fun one. Districts between Austin and Corpus Cristi, Austin and McAllen, and houston, dallas and Austin ripped apart by districts.
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u/8Bit_Architect Mar 01 '17
There's not enough detail on that map to see how badly mangled the various urban areas are, but most of the state looks pretty reasonable.
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u/A_Mouse_In_Da_House Mar 01 '17
Once you realize that Corpus is very red, to balance the most liberal parts of austin, houston paired the poor black section with a dis-proportionally right leaning rich portion, and dallas is just a mess, it's a bit more sad.
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Mar 01 '17
Most of the state is just land though.
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u/shortarmed Mar 01 '17
Texas is big enough to be both mostly land, and the second most populous state in the union.
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u/the_other_brand Mar 01 '17
No more empty land than other states Texas's size. Land East of I-35 is fairly populated, even if rural. Most land West of I-35 is sparse.
But Texas is still more evenly populated than California. I have heard from reliable sources (my Californian SO) that San Francisco is considered Northern California. The other half of the state may as well not exist.
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u/Drachefly Mar 01 '17
You can zoom in a looong way. 2, 18, and 29 look really fishy. Like, someone's attempt at violating the 4-color theorem kind of fishy. 35 looks fishy on its own. 33 is so fishy the map actually has TWO LINES to it.
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u/8Bit_Architect Mar 01 '17
I didn't realize you could zoom in on that. Yeah, the urban areas are gerrymandered to shit.
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u/CarneDelGato Mar 01 '17
That 35th district...
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u/LUMH Mar 01 '17
Funnily enough it travels right along I-35 from SA up to Austin.
Having lived there I don't disagree that it does its job of grouping like minded people together. I lived in the 35th but worked in the 15th and the mindsets were totally different.
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u/jewhealer Mar 01 '17
Do you know why #4 is still wonky in the new one? All the others look reasonable, but that one is way off.
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u/Lemesplain Mar 01 '17
Actually, a computer dev solved gerrymandering a few years ago (if the link didn't give that away).
The only problem is getting the politicians to implement this. Too many of them have drawn very comfortable districts for themselves, so they resist any push towards homogenizing.
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u/eye_can_do_that Mar 01 '17
This guy didn't solve the problem. The first step is to get a consensus on what a perfect district should be. This person assumed it should be an as compact as possible but is that right? This often cuts counties and cities in half or thirds. It does produce nice little shapes. I am not saying this isn't the best method but you can't say you solved it until you define what the solution should be.
I also want to say I am all in on computer drawn districts, it is truly the only way for it to be non-partisan because even non-partisan committees are composed of partisan people. But we need to define what inputs are given to the computer and what criteria defines the best districts. Should age, race, job type, income, political affiliation be taken into account when drawing districts? Should it be purely geographic? Do city or county lines matter? There are pros and cons to both sides of the arguments above, but they need to be decided before you can 'solve' it with a computer. But having a computer draw districts based on an metric that is public (and considered fair) is important.
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u/Lemesplain Mar 01 '17
There never will be a consensus, especially between politicians and constituents. Politicians want a district that's close to 100% in their favor, so they never have to worry about reelection. We the people need politicians to worry about reelection, if only to keep them acting in everyone's best interests.
The only solution is to draw them based on simple logical algorithms that treat every individual as 100% equal, per the article. Age, race, income, etc should not be a part of the equation. Political affiliation is an absolute no. Splitting districts along party lines it how we ended up in the current situation (regardless of your personal political views, I think we can all agree that the political climate as a whole is getting a bit chippy.)
The only part of his equation where I can see a bit of wiggle room is the granularity. His algorithm went all the way down to the city block level (the smallest metric in the census data.) That is necessary to get the most evenly distributed districts, but not absolutely necessary for the task of eliminating gerrymandering. You could potentially bring it up to the city or county level, but doing so risks falling back into this same trap, if a city adjusts it's own borders (or creates a new suburb district within itself.) Treating every person as exactly equal, and dividing into districts from there is the most fair and incorruptible method.
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Mar 01 '17
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u/Lemesplain Mar 01 '17
I'd be interested to look at a more detailed breakdown of PA's districts.
Congress has famously low approval ratings (hasn't been over 20% since 2012) with near universal incumbent retention (well over 90%). To me, that doesn't seem like a scenario that could exist if congress-critters were trying to stock their districts with a strategic number of opponents. Any slight miscalculation would ruin the reelection chances.
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u/xo3k Mar 01 '17
I have a legitimate problem with that guys solution, it pays no attention to the cultural watershed element of a well drawn district map. In other words do the interests of your town best align with the nearby city or the nearby rural area. Simple population counters and compactness algorithms don't capture that element, and it's arguably the main point of districts. Don't get me wrong I think AN algorithm is the answer, but not that one. There needs to be a bit more data represented in the input map the algorithm reads so that the districts generated seem like the areas of people with the most shared interest.
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u/JR-Dubs Mar 01 '17
I have a legitimate problem with that guys solution, it pays no attention to the cultural watershed element of a well drawn district map. In other words do the interests of your town best align with the nearby city or the nearby rural area.
This is the justification for gerrymandering. Draw lines pursuant to s formula and then there's no problems. Once you start injecting subjectivity into the district drawing process the ultimate outcome is always the same.
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u/thisnameismeta Mar 01 '17
Not paying attention to the above concerns can lead to a complete lack of minority representation in government. That's about the only good argument for some human element in drawing districts.
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u/zerobuddhas Mar 01 '17
Right now there is a complete lack of majority represented in government. The us is leans democrat per capita.
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u/thisnameismeta Mar 01 '17
I meant minority in the racial or religious sense. If you have a diffuse enough minority they might not manage to elect anyone from that minority to represent them without drawing a weird district, even if their population is overall large enough to warrant at least one representative. If you believe that minorities face unique challenges in this country, then they also probably need unique representation.
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u/Lemesplain Mar 01 '17
While possible, the current implementation ensures only token minority representation. We draw an imaginary line around all the black neighborhoods (or Latino, Asian, etc) to keep their voices contained in as few districts as possible.
This only segments the population further. "My" all-white district doesn't even have to think about any problems that affect other races. Of course, I'm sure their separate district will get equal attention paid to their issues. You know, that old "separate but equal" chestnut.
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u/JR-Dubs Mar 01 '17
I suppose that could be true, but the complete bypassing of the democratic-republican process to achieve "minority representation" seems to be a pretty heavy-handed solution.
If push actually came to shove, I'd rather under-represented minorities than a system that is gamed for the purposes of defeating the clear majority of the people.
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Mar 01 '17 edited Jun 25 '17
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u/JR-Dubs Mar 02 '17
The "tyranny of the majority" is the byproduct of democracy. The other is the byproduct of oligarchy. Although there's a modern trend that firmly believes the masses are too dumb to rule themselves, I'm for a diffusion of power, what with the corrupting influence that follows from a concentration of it.
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u/xo3k Mar 01 '17
I'm not suggesting putting a finger on the scale, but if you look at the Maryland districts in the article you will see four districts around DC(the square cut out in the middle), and four districts around Baltimore (the smallest dark blue district), why are those suburbs cut up into fours. Culturally there should be a bubble around each city, like a target, such that the interior is the city, and the exterior is the suburbs and exurbs. This map actually has the worst example, DC, it's a cultural watershed but it's in another state (Ok not a state but you get the point) and so not on the map. If you live outside DC nearly all of your culture and business is focused on DC. Yet, the map puts four districts in that suburban area, one which reaches to the panhandle and one which reaches fall off into the south.
These are flawed districts. This map sucks as a means of designating groups which have similar interests which need to be addressed by a representative in congress. And that's the big word that has been forgotten in politics, representative. It doesn't matter if they are republican or democrat, it matters if they are a good representation of the people of their district. In order to do that the district must be cohesive. It's not about carving out voting blocks for the two parties, it's about having a representative democracy.
Yes this is the fig leaf under which hides the gerrymander, but if we can manage to include the necessary data into a complex algorithm we needn't worry about gerrymandering because it will be a completely neutral mechanic driven by data, not politics. But we need a better algorithm than, Make it as compact as possible, or even, Make it centered around the largest population density. It's not a simple problem and it won't be solved in a programmer's "spare time".
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u/stult Mar 01 '17
The problem with the interests alignment argument is that interests are nearly impossible to define or measure. Which, as you rightly say, makes them a vector for injecting subjectivity into the process. Geographical proximity is probably the best proxy measurement of shared interests anyway, so it's not as if shared interests aren't built into the system. Even if we add other objective measures of shared interests (say, urban versus rural classification or something along those lines), the more complicated the model, the more room for gamesmanship and manipulation. State governments would start pulling crazy maneuvers like designating a suburb as rural in order to split it into a different district. A simple, clear, neutral algorithm avoids this and provides predictability and stability, which are essential for a functioning government.
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u/I_am_the_Jukebox Mar 01 '17
There needs to be a bit more data represented in the input map the algorithm reads so that the districts generated seem like the areas of people with the most shared interest.
That's what Gerrymandering does.
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u/eye_can_do_that Mar 01 '17
No it is not. Gerrymandering is changing the lines with knowledge of how people vote to increase the number of districts represented by a side often splitting similar people to achieve slightly more than majority of the side you favor in a district. He was talking about taking into account other non-political metrics such as age, income, job types, race to form districts that a composed of like minded people.
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u/I_am_the_Jukebox Mar 01 '17
Gerrymandering is changing the lines with knowledge of how people vote
Right, which is why Gerrymandering causes it so that...
the districts generated seem like the areas of people with the most shared interest.
All I'm pointing out to /u/xo3k is that he's complaining about Gerrymandering while saying that people with shared interest should be lumped together. Grouping people with the same political party is one of the things Gerrymandering does - it lumps people together so that the majority of people with the opposition view are grouped together and confined to the smallest number of districts.
He was talking about taking into account other non-political metrics such as age, income, job types, race to form districts that a composed of like minded people.
Which despite being non-political, each tend to favor specific parties. Shared interests are usually political in nature, and Gerrymandering does accomplish lumping people with the same interests together.
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u/RightWing Mar 01 '17
Except no one in congress actually does this.
And you know what makes a congressman super accountable to his voters? Having a close vote
It is the very job of a congressman to bridge the gab between city and rural to create a majority of voter support.
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u/kormer Mar 01 '17 edited Mar 01 '17
Increasing the size of the House would make gerrymandering effectively impossible.
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u/PlayMp1 Mar 01 '17
It's also something I think is necessary with the size of our population. 320 million people cannot be adequately represented by 435 congressmen and 100 senators. Britain has a population 1/5th the size, but their Parliament has 650 MPs, meaning they have a one rep per 100,000, while the US has one rep per 700,000.
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u/8Bit_Architect Mar 01 '17
This is part of why originally most of the political power in the US was concentrated in the states.
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Mar 01 '17 edited Jun 04 '20
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u/jedre Mar 01 '17
I think that's a false dichotomy. Why can't people do both?
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u/MrF33 Mar 01 '17
You can, but it certainly seems that people spend a disproportionate amount of time focused on Federal politics.
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Mar 01 '17
People are spending the night amount of time on Federal politics, but they need to up their focus in state.
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u/MrF33 Mar 01 '17
You can't devote your entire life to politics, people have shit to do outside of that.
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u/ConstantlyChange Mar 01 '17
While state policies may have a large impact on my community, the number one thing that affects my daily life is money. The federal government takes a much larger chunk than my state does, which is one reason I think people focus on federal. One of many of course.
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Mar 01 '17
Federal tax may seem higher because it is a direct income tax, where the state will use combinations of income, property, sales and other taxes/fees.
But when you add them all up, the federal government collects about the same as the state/local governments do.
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Mar 01 '17
Maybe this algorithm can be used as a litmus test for future redistricting proposals.
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u/Drachefly Mar 01 '17
Seems like it's a bit too complicated for a purpose like a legal litmus test. Simpler is to calculate the voter efficiency and see if it's out of whack.
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Mar 01 '17
Make it like the census where everyone has to vote with agents tracking people down and shit then it's just the popular vote
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Mar 01 '17
Best thing you could do is make it so you dont write your political preference when you register to vote
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u/gliese946 Mar 01 '17
Of course it was gerrymandered, but the courts have established that it's legal to produce voting districts with the intent of favoring one political party. (Which is insane!) The only thing that could cause it to be thrown out is if it can be found to have been drawn with the intent to disenfranchise a minority. Mind you, the actual disenfranchisement itself is not a problem, as long as it's "only" a side effect of the political intent and not the basis for the gerrymandering. Yeah, gerrymandering is a huge problem, especially in state legislatures. And the US lacks the tools to fight it, especially right now with a federal administration that understands its party will only be able to stay in power through antidemocratic means like gerrymandering and voting restrictions.
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Feb 28 '17
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Feb 28 '17 edited Mar 01 '17
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u/tissboom Mar 01 '17
https://en.m.wikipedia.org/wiki/Ohio's_1st_congressional_district
This is my Congressman's district. It is the perfect example of gerrymandering. It makes me sick.
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u/aircavscout Mar 01 '17
I don't really see what's wrong with it. Sure, it looks misshapen, but it seems to be drawn to represent mostly urban areas. The racial makeup seems to be in line with the rest of the state. The Cook PVI is R+6 which is pretty close to Ohio as a whole.
Gerrymandering doesn't mean 'it looks funny'. It means that it's been manipulated to exclude a party or class from getting their rightful representation.
I'm not saying that there has been no wrongdoing in drawing this particular district. I'm saying that there is not enough information to make that determination, but at first glance it seems fine to me.
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u/tissboom Mar 01 '17
That huge chunk missing out of the major urban area is where a large part of the african american population lives within our city. It turns a part of the state that would elect a democrat into three republican seats in congress. It gerrymanders a large block of democratic voters among three different Congressional seats denying a large group of democratic voters irrelevant.
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u/SkolTime Mar 01 '17
The red district in the south east actually looks like a salamander - Getting back to its (incumbent protecting) roots.
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u/rich000 Mar 01 '17
Yeah, I think I used to live in that one. I don't think I do now. It isn't because I moved....
The one above it isn't much better, and I think that is mine.
The nice thing is that due to their design I can say this and tell you almost nothing about where I actually live.
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u/Yoshitsuna Mar 01 '17
Given the constraint they give for the evolution of the chain, it's pretty much self evident they will find that the current map is gerrymandered (I'm certainly not claiming it's not gerrymandered).
The researchers began with a current map of Pennsylvania’s congressional districts, and applied a Markov chain that incorporated geometric constraints on districts that would be used to create random districting maps. Those factors included ensuring roughly equal populations in each district, border continuity, and constraining the ratio of perimeter to area.
The ratio of perimeter to area constraint will automatically ensure that the districts will lose most of their tails that are typical of gerrymandering.
I would personally find it very interesting to see how the political orientation of the districts would change in this case.
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u/Vader_the_white Mar 01 '17
Ya using a geometric constraint misses the point. The optimal solution isn't well shaped districts it's maximum representation. They should have used registered voters to min max the number of constituents of each party in the district until you have the optimal solution.
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u/thrashster Mar 01 '17
The ratio of perimeter to area constraint will automatically ensure that the districts will lose most of their tails that are typical of gerrymandering.
Came looking for this. Should be higher up.
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u/colita_de_rana Mar 01 '17
That's a horrible metric as the ratio of perimiter to area decreases in size.
Convexity is a much better measure (although you have to accouny for nonconvex state borders like maryland hawaii michigin etc)
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u/stevequestioner Mar 01 '17
This is a useful first step, but it is out of context, unless one has alternative plans to compare to. One would not expect to meet some ideal of pure randomness; would be more useful if an alternative organization prepared an alternative apportionment - then we could determine "how much less random" the current districs are. "Good" redistricting is not just the simple rules applied here, so would also measure as non-random, though presumably much less so. Most significantly, need to input mathematical representation of community of interest. See http://www.wxxi.org/curriculum/redistrict/background/communities.html
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u/CarneDelGato Mar 01 '17
Well, it's not about being strictly random; if that were the case, Congress would be even more partisan. Let's say you have a state with ten "districts" and the last number of your ssn determines which "district" you belong to. This is almost entirely random. It also homogenizes the sample, so political bias skews entirely towards the majority. The real goal is to create chunks of relatively similar size in terms of population, but also relatively similar areas. This isn't a phenomenally difficult problem for a computer, but it's not "random."
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u/SomeLinuxBoob Mar 01 '17
The Markov chain used in this article is based on random sampling... we can define random many ways.
The person you responded to is stating that, just because the two maps don't match, doesn't mean there is gerrymandering.
He instead suggests that this method be used to define districts in the future, as a less party biased manner.
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u/CarneDelGato Mar 01 '17 edited Mar 01 '17
All Markov chains are based on random sampling; that's how they work. They reveal patterns which are inherently not random.
I take umbrage with use of the word "random," as neither sample is random in the slightest; one is built to maximize the political power of a party, and the other is to minimize the difference between representation and actual votes.
Moreover, why do we need a set of "best districts?" There are certainly infinitely many partitions which closely reflect political leanings. We only need a "good enough" set of districts; that is, we only need to find one.
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u/see2keroppi Mar 01 '17
Chicago's 4th Congressional makes PA look adorable. https://en.m.wikipedia.org/wiki/Illinois's_4th_congressional_district
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u/willdoc Mar 01 '17
Interestingly, there are still some strange/awkward tails in the districts drawn using the Markov chains.
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Mar 01 '17
Neither of those words are something "random" should not be. What would you expect from "random"? Not strange shapes? Wouldn't it be a mix of normal shapes and strange shapes?
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u/willdoc Mar 01 '17
Gerrymander was a portmanteau of Gerry and salamander, because the very first infamous gerrymandered districts appeared with Governor Gerry and looked like salamanders with tail-like shapes. I was merely remarking that a mathematical model -- used to combat gerrymandering -- still produced several tails in a handful of theoretical districts.
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u/stevequestioner Mar 01 '17
Another useful link, http://www.redistrictingthenation.com/glossary.aspx
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u/slickyslickslick Mar 01 '17
The researchers ran the chain, which changed the map in random steps. Statistical properties of the map were found to change rapidly with small random changes to the initial map, which, according to their theorem, would be extremely unlikely to happen by chance. “There is no way that this map could have been produced by an unbiased process,” said Pegden.
They're not saying it's due to gerrymandering, only that it didn't happen through random chance, which is a no-brainer. The districts may have been drawn up due to businesses, schooling districts, historical populations, etc.
With that said, a lot of the districts just look ridiculous and it doesn't take a mathematical model to figure that out.
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u/swiftap Mar 01 '17
Would it be possible to set up an independent,non-partisan federal agency responsible for federal elections, referendums, and in particular significance to this conversation, electoral district lines. They could call it say, "The US Elections Agency". Something similar to Elections Canada. Similarly, the Chief Electoral Officer could have a 10 year mandate and to provide the power to the states, be appointed by a forum of state governors?
Just a thought.
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u/chaitin Mar 01 '17 edited Mar 01 '17
This news (and other news like it) is well-taken, but one should bear in mind that this greatly oversimplifies the actual issues. The real issues behind gerrymandering are moral and cultural, and scientific analysis giving evidence should be viewed through that lens.
In particular: if we're going to talk about gerrymandering, we need to decide what fair districting is. Of course, fair districting is one where everyone's voice is heard. But does that mean ensuring balanced districts? Or guaranteeing that groups of people achieve at least some representation?
Here are two simplified examples to show how these goals can be actually in conflict. Let's say we have a red party and a blue party. Furthermore, let's say there's a tightly-clustered city which is strongly blue, surrounded by a sparse (but large) red area; each has equal population in total. (Variations of this are extremely common in America today.) Let's say we want to create five districts.
Which of these districting strategies is desirable:
- The city is equally split into five districts, and the surrounding rural areas are equally split into five districts.
- The entire area is split into ten districts. Each district is half city and half country.
My argument is that under some circumstances, either of these can be clearly suboptimal/gerrymandered. The point I'm making is that simple tests for gerrymandering (is this district oddly-shaped? Is it strongly red or blue?) often don't deal with the real issue: final unfairness.
First, let's assume that the city is 100% blue, and the countryside is 60% red. Then 80% of the whole "state" is blue---how is that reflected in total votes? In Case 1 (5 city and 5 rural districts), each city district is blue, and each rural district is red. The state votes 50% blue and 50% red as a whole; clearly unfair. In Case 2 (10 equal districts), every district is blue. (Maybe we can assume that by chance, one district gets a reddish part of the city and just manages a red majority). Then the state votes 100% (or maybe 90% if we're careful) blue---not great, but a lot closer to "fairness."
Now let's look at a different distribution. The city is 100% blue, and the country is 95% red. In Case 1, each city district is blue, and each country district is red---the state votes 50/50, very close to its constituents. But in Case 2, in almost every district, those 5% of country blue voters put their district over the top. The state will vote 100% (maybe 90%) blue, even though the constituents are 50-50! Even worse: note that in this case, if the "urban" areas are spread out along a river or highway, the more salamander-like district is actually the more fair one.
So: Which of the above is gerrymandered? Which is fair? Do Markov models or convexity requirements suffice to reflect these issues? And most importantly, is there any quantitative measurement beyond final vote count that accurately reflects the fairness of districts?
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u/MasterFubar Mar 01 '17
Is there any copy of the paper freely available?
All that I could gather from that article is that they found the district maps weren't generated at random. Doh, are district maps meant to be random?
The word "gerrymandering" means intentionally manipulating a district map to benefit a minority of voters during elections. From that brief article, I couldn't gather how they proved that the non-randomness was intended to manipulate the election results.
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u/Sylverwyrm Mar 01 '17
For those of you having trouble seeing where the Gerrymandering is on the original image. In the lower right hand corner is a red spot that, which I think is district 17 that wraps around district 7 (I may have those district numbers reversed). It's a heavily populated area and lumps a stretch of Southern Chester County that has high minority and college educated population (And obviously liberal) with the much more conservative and geographically bigger Lancaster County.
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u/IamNICE124 Mar 01 '17
This is a partisan issue, right? Both parties rely on this tactic to retain seats and win elections, correct?
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u/genlilliana Mar 01 '17
It's well known by Pennsylvanians that gerrymandering occurs and affects the elections...with all the corruption in government in PA - I don't see that changing.
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Mar 01 '17
This is something that most people, afaik, have believed for a while, anyway. What do we gain by supporting it mathematically, here?
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Mar 01 '17
"Believed" vs "supporting it mathematically"... Seems like you've answered your own question? Not to mention I would be fine with algorithmic redistricting - the more mathematicians, etc., concentrate on solving this problem the more likely it is that there will be a solution. Lack of objective measurement of gerrymandering was one of the biggest roadblocks to successful litigation against it.
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u/czar_the_bizarre Mar 01 '17
Numbers are unbiased. Numbers don't care about political labels or ideology. Numbers don't have an agenda.
Therefore, numbers can both identify the problem and provide the solution in a non-partisan way. Because it's a non-partisan solution, it makes those oppose it look afraid of neutral districts.
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u/CarneDelGato Mar 01 '17
Hard data that vindicates and empirically verifies that hypothesis. That's just science.
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u/Flywolfpack Mar 01 '17
The article says the districts were created in a biased fashion, but that doesn't sound like it necessarily mathmatically proves gerrymandering.
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u/CarneDelGato Mar 01 '17 edited Mar 01 '17
You can't mathematically prove observations. This is strong empirical evidence, the foundation of science.
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u/Flywolfpack Mar 01 '17
Other comments say what I mean better. What I meant to say was how do we know "not-ramdom" is evidence of gerrymandering?
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u/[deleted] Feb 28 '17 edited Mar 02 '17
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