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An impossibility theorem for gerrymandering

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Re: An impossibility theorem for gerrymandering

#21

Post by indubitable »

I think this indirectly hints at something much more fundamental: district based plurality does not make sense as an election system anymore.

I think an eye opening example is to consider a hypothetical single state with 10 representatives. This state has a population, perfectly well distributed, of 35% democrat, 30% republican, 20% libertarian, and 15% green. And we draw our districts up with absolutely no bias whatsoever. What 'should' the election results be? I think any logical person would say about 3.5 democrats, 3 republicans, 2 libertarians, and about 1.5 greens. What we get in reality? 10 democrats as they win a plurality in each and every district. 0 gerrymandering, 35% of the support, 100% of the seats.

To get our above example to have the logical results we want, you end up having to create really absurd districts that would completely dwarf any sort of gerrymandering of today. So then the question is quite obvious. Why don't we do at large proportional elections instead of district based plurality elections? If a state has 10 representatives then any party is guaranteed at least 1 seat if they get 10% support, 2 for 20%, and so on.

In the past when politicians and the people were much closer, I think districts made a lot more sense. You were voting for somebody who you knew or were at worst split by the most minimal degrees of separation. But today this isn't true. The average congressional district is now up to 710,767 people [1] (as of 2010). In 1790, at the time of the first US census, the average district size was 37,082. Times have changed, but our electoral system has not.

[1] - https://en.wikipedia.org/wiki/List_of_United_States_congress...

Re: An impossibility theorem for gerrymandering

#22

Post by Retric »

dragontamer wrote: post #17
Retric wrote: post #6

Earlier quoted context omitted.

If votes are 80-20 then it's not necessarily possible or reasonable to draw 80 vs 20 winning districts.

Which states are 80-20 in America? Maryland is an example of a highly gerrymandered state (towards Democrats, although there are many Republican examples too). Maryland voted 60.5% Clinton / 35.3% Trump, which suggests that they have (roughly) 2 Democrats for every 1 Republican in the state. However, due to the significant gerrymandering in Maryland, there is ONE Republican and SEVEN Democrats in the House. That's ce…

There are actually more extreme examples. Consider, Hillary Clinton got 90.9% of the DC vote Trump got 4.1%, I am not sure how you could slice up DC to get 10% Republican representation.

In Maryland's case it might be able to make 2 districts Republican, but that's assuming a very concentrated geographic minority which may or may not actually exist.

IMO, If we really want proportional representation then we should use a proportional system.

Re: An impossibility theorem for gerrymandering

#23

Post by sova »

For reference, there is a NY Times article about the plague of redistricting and also a simple excel tool that someone made to make this very easy: https://www.nytimes.com/2017/08/29/magazine/the-new-front-in...

As a human who takes pride and joy in the Constitution and its tenets I find the crowbar-able gap space of redistricting an important valley of electoral attention that needs ample light of attention.

Re: An impossibility theorem for gerrymandering

#24

Post by catpolice »

At this point I feel like it's worthwhile to remember to why we even have districts.

We could, in principle, get rid of the districts and just have some kind of statewide scheme for electing representatives proportional to the outcome of a popular vote. The idea behind retaining districts, as far as I understand it, is that people in similar locales will often have very correlated interests (e.g. with regard to decisions that affect that area) and that choosing representatives from particular locales is supposed to guarantee that people in that area are represented (and make the representatives to some degree beholden to them).

Ideally, we'd split the states into districts in a way that doesn't deviate from overall proportional representation very much, hence the idea of the efficiency gap. So gerrymandering can break that efficiency constraint.

But the notion of geographic correlation of interests makes it such that the population is unlikely to be distributed in the kind of uniformly random way you need to get weirdly shaped, efficient districts, and conversely having weirdly shaped districts at all effectively assumes that geographic correlation of interests isn't an important factor.

In other words: if we have to make weirdly shaped districts to maintain efficiency, then the assumptions that caused us to require districts in the first place probably fail and we should just ditch them.

Re: An impossibility theorem for gerrymandering

#25

Post by dragontamer »

cousin_it wrote: post #9
dragontamer wrote: post #4

So the question is if "Minimizing Efficiency Gap" is what we should be aiming for. Its a solid proposal, but I guess its up to the courts to decide if "Efficiency Gap" is a good metric. I guess I'll be interested in hearing the arguments as they come up.

It seems to me that a system with zero efficiency gap would be equivalent to one big election with proportional representation. If that's what people really want, why talk about voting districts at all?

Because certain issues are geographical in nature, especially at the local level.

Should a new highway replace the housing development over there? Well, people who live close to that housing development might care one way or the other (Noise complaints, Ecological issues, Traffic Issues). People who live very far away from that center probably don't care at all. And the people who live in the housing development (who will be forced to move out), especially renters who probably won't be properly compensated, will care the most.

The placement of schools, the budgets of police, the design of zoning regulations (in particular "Enterprise Zones" of lower taxes to encourage business development in some areas)... these all are innately local issues.

Re: An impossibility theorem for gerrymandering

#26

Post by dragontamer »

Retric wrote: post #22
dragontamer wrote: post #17

Earlier quoted context omitted.

Which states are 80-20 in America? Maryland is an example of a highly gerrymandered state (towards Democrats, although there are many Republican examples too). Maryland voted 60.5% Clinton / 35.3% Trump, which suggests that they have (roughly) 2 Democrats for every 1 Republican in the state. However, due to the significant gerrymandering in Maryland, there is ONE Republican and SEVEN Democrats in the House. That's ce…

There are actually more extreme examples. Consider, Hillary Clinton got 90.9% of the DC vote Trump got 4.1%, I am not sure how you could slice up DC to get 10% Republican representation. In Maryland's case it might be able to make 2 districts Republican, but that's assuming a very concentrated geographic minority which may or may not actually exist. IMO, If we really want proportional representation then we should us…

DC is a single city and doesn't even have one representative in Congress (Okay, they nominally have one. But she's non-voting so.... that's not really useful). They're technically a US Territory and have no more power than say Puerto Rico.

So once again, if you're talking about US Representatives and Voting Districts, it only makes sense to talk about well... Voting Districts. Name me one US State with 80/20 split and more than 1 US Representative. Ultimately, your hypothetical doesn't exist!

---------

That's the cool thing about politics: its real. There's no need to make up hypotheticals when we can just draw from the real world.

FYI: the discussion at hand is about US Representatives, and not about the Electoral College. Washington DC is therefore irrelevant, as it has no representatives. Washington DC does get 3 Electoral college votes, but that has nothing to do with Gerrymandering.

There's a variety of states who have "Representatives At Large", such as Wyoming, which are basically immune to Gerrymandering. The population is so low that Wyoming only gets 1-Representative, so the entire State is the whole district. There's really no "fair" way to cut up a single Representative (its all or nothing), but that's mostly due to the very low population of these states.

Basically, Gerrymandering can only be an issue in a state with more than 1 Representative.

Re: An impossibility theorem for gerrymandering

#27

Post by cmac2992 »

sova wrote: post #16

The Supreme Court (id est The Highest Court of the Land) is currently evaluating if they can rely on an algorithm to detect Constitutionality of district shapes. You're kidding, right? As a computational scientist this is concerning to put it mildly. Trying to ensure proportionality in representation... is that the intended goal? Is this even a meaningful pursuit in a bicameral system? The Supreme Court makes rulings…

From my understanding, the Baker v Carr in 1962 decision enabled federal courts to intervene in and to decide redistricting.

Back in the day redistricting was even crazier. You could just draw an arbitrary number of districts with arbitrary population sizes. That seems bad on the surface. With this system, election outcomes could potentially be entirely determined by how districts were gerrymandered.

The efficiency standard seems like trick to get closer to proportional representation. All of this comes down to the 14th amendment being "one person one vote" rather than something like "all votes must have equal weight". A small language that has made things really complicated.

IMO just switching to proportional representation is a much cleaner solution. But the efficiency standard seems like a decent solution to keeping races competitive and from being severely gerrymandered.

Re: An impossibility theorem for gerrymandering

#28

Post by sova »

weeksie wrote: post #2

Totally. This is why in the more recent gerrymandering thread I was making such a big deal about the efficiency gap rather than geometry for detecting this stuff. Geometry is just a flawed heuristic for a multitude of reasons. That's why the efficiency gap is so exciting as a measure.

Looking at the paper, counting the number of "wasted votes" is actually the most solid metric it seems!

Re: An impossibility theorem for gerrymandering

#29

Post by sova »

notfromhere wrote: post #15
tveita wrote: post #13

It's strange that there's so much focus on district shapes, when any voting system with proportional representation would make gerrymandering pretty much ineffective. Every voting system has its flaws, but the US system seems to have particularly few advantages.

stable oligarch control is pretty much the only advantage

Tip my hat to you dear friend.

Re: An impossibility theorem for gerrymandering

#30

Post by sova »

awjr wrote: post #7

I suspect Gerrymandering isn't uniquely a US problem. I do a lot of UK Census spatial analysis and the district centroids that are used create problems. In the article the 'ear muffs' shape would create a centroid for the voting district outside of the district, given that the shape of the district was designed to give a certain ethnic group a voice, whereas the process for creating districts in the UK are done usual…

Fuzzy circles! Great idea. That, or repeated boundary drawing that brute forced every possible district combination and gave a probabilistic result of elections based on where districts were drawn.
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