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The Very Hungry Gerrymander

October 4th, 2012, 12:00pm by Sam Wang

Summary: My analysis indicates that redistricting has given Republicans an advantage of about 1.2% in national popular vote margin compared with pre-2010. In a close national Congressional race, which we have this year, this translates to an advantage of 13 seats. The effect is more than I was expecting.

Left: Eric Carle's caterpillar. Right: NC 12th District Before I update my House prediction, it is necessary to quantify two reader concerns: incumbency and redistricting. Today I quantify the net total effect of redistricting from 2010 to 2012, and give the results of analysis that sharpens my previous estimate of incumbency effects.

For the first time in many decades, Republicans have dominated the post-Census redrawing of Congressional districts, controlling twice as many districts as Democrats. Do the resulting changes lead to a structural advantage, i.e. will the Democrats have to win more than 50% of the two-party vote to achieve a near-tie in House seats?

Many of you are convinced that the resulting tilt to the playing field is large enough to definitively rule out a Speaker Pelosi in 2013 – a big thumb on the scale. Some commentators share your view, including Rasmussen Reports. However, Congress-watcher Stuart Rothenberg says the new maps are “a wash.” Indeed, this was an assumption in my previous prediction regarding House control. Who’s right, me and Stu – or you and Ras?

Ignore the jagged appearance of the black curve, caused by roundoff in the 2008 voting data.

This summer Charlie Cook wrote:

The Cook Political Report rates 211 House seats as solid or likely Republican, compared with 171 as solid or likely Democratic. If the 24 toss-up races split evenly between the parties, Democrats would score a net gain of just a single seat. Even if Democrats held everything in their solid, likely, and lean columns and also won every toss-up, they would still need to take two-thirds (12 of 18) of the districts rated lean Republican to win a majority. That’s a pretty unlikely scenario, absent a strong wind at their backs.

This kind of fine-grained analysis takes a lot of knowledge, but is hard to reduce to a single quantitative insight. I set out to make an estimate of redistricting’s effect in units of popular opinion – reminiscent of the Popular Vote Meta-Margin for the Presidential race.

To make that estimate, a key concept is the Partisan Voting Index (PVI), developed in 1997 by Cook. The PVI is defined as how partisan a state or Congressional district leans compared to the country as a whole. For example, PVI = R+2 means that on average, a Republican candidate will typically get 2% more of the popular vote than the national average.

So on average, the PVI should be zero, right? No. Changing this average has been the goal of Republican-dominated state legislatures. If they can corral lots of Democrats into fewer districts, then it will take fewer Republicans to win the remaining districts.

Thanks to redistricting geeks on both sides of the aisle, I did not have to compile PVI’s. Republican activist David Lasdon helpfully provided me with a spreadsheet of post-redistricting PVI’s. He calculated it using Dave’s Redistricting App, a software tool created by computer scientist and Democratic activist David Bradlee to let individuals create their own Congressional districts. I also have numbers from the redistricting team at DailyKos Elections. These give very similar results. The graphs below come from Lasdon’s data.

I sorted the PVI’s and plotted histograms:

In this format, it is not easy to see what the net effect is. A better approach is the cumulative histogram:

Pre-2010 seats-vs.-PVI curve; red * 2002-2010, green *1992-2000, black o 1946-1990

Here, the vertical quantity is how many pre-redistricting Congressional districts were at least X% more Republican-leaning than the value on the horizontal X-axis. The most Republican-leaning district shown is R+10%, and about 120 districts are more Republican than that. At the right is D+10%; 320 seats are less Democratic-leaning, i.e. 115 seats are more Democratic-leaning.

Actual election outcomes are superimposed, converted to match the curve. Red asterisks show 2002-2010, which should have been predicted most strongly by the districting curve. The fit is not particularly good, though unfortunately we lack data at the crucial 217.5-vote point. Overall, it seems that voters lean slightly Democratic in their Congressional preference compared with their Presidential-based PVI. This was even true when Republicans had the majority (the points above the horizontal red line).

Blue asterisks show 1992-2000 and black circles show earlier periods, 1946-1990. The general cloud of points is fairly fat, so that while redistricting must be taken into account, it is just one of many competing factors. As I have written before, until 2012, an evenly split House popular vote would have led to an approximately evenly split House.

However, there is something we can answer: how much did the playing field change for the 2012 elections? In combination with what we know about pre-2012 outcomes, this would be a very useful quantity. We can do that by comparing the cumulative histograms:

The black curve shows data pre-redistricting, and red shows post-redistricting data. The curves are nearly overlapping…or are they? Let’s look closer. Zoom in to the middle 100 of the PVI’s:

Ignore the jagged appearance of the black curve, caused by roundoff in the 2008 voting data.

The main point is this: this midrange is shifted to the left for the new districts. As a group, these middle 100 districts are somewhat more Republican-leaning than the middle 100 districts from 2008. They are not necessarily the same districts, but that does not matter for this level of analysis. In other words, at any given level of national partisanship, the number of districts that lean Republican is greater after redistricting.

Alternately, look at the shift in the vertical direction. The more people vote Republican on November 6th, the further right we will be on the axis, as each district’s PVI is overcome. The red curve is above the black curve, which means that the same national vote will yield more Republican seats. This is the structural advantage from redistricting. It is largest for GOP caucuses smaller than 254 seats – in the range where it matters.

How can we quantify the advantage in terms of national popular vote? That can be done using the horizontal distance between the curves – how far one curve would have to be shifted to align it with the other curve. The average shift over the range shown is R+0.62 +/- 0.06% (mean +/- SEM). In terms of seats, use the vertical distance to get a redistricting advantage of R+6.3+/-0.6 seats.

To get effective vote and seat margins, multiply these numbers by 2. Democrats will need to win a 1.24% larger margin to achieve the same number of seats they would have gotten in 2010. And for a given popular vote split, Republicans will have a larger House margin by 12.6 seats on average.

So: in terms of national popular vote margin, the Congressional 2012 new redistricting advantage is R+1.2+/-0.1%.


Finally, a brief note on incumbency. Although incumbents walk into the general election campaign with an advantage, as shown by Andrew Gelman, much of that advantage should already be captured by the generic Congressional ballot.

Previously I estimated the incumbency advantage this year, averaged over all districts, as R+1.3 +/-1.8%. This is based on 1996-2010 data. Based on 1946-2010 data it becomes R+1.3 +/- 0.4%. This is a second net potential advantage for Republicans.


The sum of these is R+1.8 +/- 1.0%. This is the amount by which Democrats must win the popular vote in order to have approximately even odds of winning control of the House of Representatives. I previously assumed an advantage of R+1.3+/1.0%. The next House prediction will use the new calculation.

I thank Nathan Persily and Steven Schultz for discussions. I also thank David Lasdon and Daily Kos Elections for their calculations. This kind of geekery is bipartisan. Lasdon seemed to think I was a political scientist, and wrote: “I look forward to being a footnote in a paper I’ll never read.”

Tags: 2012 Election · House

44 Comments so far ↓

  • Jacob Hartog

    Don’t know much about Political Science (as Sam Cooke once said) but this looks like the beginnings of publishable work. David Lasdon might be right!

  • JamesInCA

    Do you prefer the incumbency advantage based on 1946-2010 over 1996-2010 because of the larger number of samples used to calculate it? My sense of things is that the social and media context of elections has changed so much over the longer time period that more weight ought to be accorded to more recent elections. Someone who was a new, 18-year-old voter in 1950 is now 80; these folks comprise just a percent or two of the population.

    • Sam Wang

      It’s not individual voters – it is the macro effect of incumbency. So your argument does not make sense.

      The time period was chosen to get a more accurate estimate. When a parameter like this is 1.0 +/- 2.4%, as it is for 1996-2010, it is better to assume it is zero. In fact what I did minimizes the ratio of the uncertainty to the parameter. That’s a criterion for good parameter estimation.

  • Joel

    Wow, that’s a pretty wild redistricting effect. It shows the power of controlling the state legislatures.

  • KEL

    Is there an algorithm or set of rules that would, lead to the creation of less biased districts? The use of power to maintain power seems unhealthy for a democracy. It would make sense for us as a society with advanced geographic/ mathematical tools to minimize this bias.

    • Sam Wang

      Indeed there are such algorithms! Many states are going down this road. Hmmm…would you like a guest post on this subject?

    • JamesInCA

      I would like one.

    • KEL

      Yes that would be interesting

    • xian

      yes, please. no need to show my comment. just wanted to add my vote!

    • Jfield

      A guest post would be great Sam. Hopefully it could address if there is any meaningful political bias in the states pursuing this (it would seem disastrous for democrats if the stats that consistently lean democrat in the house of reps are the ones leading this trend).

      My hunch is that states with a strong bias towards one party (and thus lopsided benefits from gerrymandering) will tend to adopt unbiased approaches as soon as the less benefited party gets power. States that can be easily gerrymandered either way will tend to ping pong between biases rather than becoming unbiased. I may be too cynical but I doubt it.

    • wheelers cat

      yes please also. that would be fascinating.
      The trend for population centers to be majority-minority markets is already skewing the electoral college. That is why Texas might flip sooner than later.

      Texas contains nearly a quarter of the nation’s “majority-minority” markets — 25 of 106. Next are California with 17, New Mexico with 13 and Mississippi with 10.

      umm…..should districts be fractal? or just geographical?

  • Paul K2

    Does the constitution allow alternative methods for allocating a state’s congressional seats?

    For example, if a state has only two congressional reps, can the state elect to make both seats “at-large” seats?

    A big improvement would combine multiple congressional districts, with the candidates competing for the available seats. For example, in Pennsylvania, the state could be split into six areas (each with 3 seats), with the voters allowed to vote for three candidates (or even four), and with the top three elected. In the state of Washington, two areas could have 5 seats each. Nevada could have all four congressmen/women at large and represent the entire state.

    This would also contain a big opportunity for 3rd party reps.

    This would:
    – Eliminate a lot of incumbents in “safe districts” who no longer may be the best candidate.
    – Reduce the amount of redistricting games and impact.
    – Elect candidates who have the best interest of the entire region or state, instead of some district big shots.
    – Probably get rid of a lot of divisive candidates like Michele Bachmann. Most winners would likely need to get at least some voters from the other party.

    Sure sounds a lot better than the system we have know. If the Republicans don’t want to give up their current advantage, then give them a one percentage point “handicap”; it would be worth it to get rid of the current bunch of crackpots and incompetent congressional reps (from both parties).

    • William

      I believe that at-large elections have actually happened in the past for Congressional districts but it was related to some weird circumstances.

    • Steve In Colorado

      I believe the ‘at large’ house seats were banned by the voting rights act. (except in states with only 1 rep)
      It would be nice to have a truly objective way to apportion. But at least take comfort that by 2018 the gerrymander should be mostly weakened…

  • Eric McGhee

    Why not use district-level data to analyze a district-level phenomenon? You’re forced to adopt all kinds of untested assumptions, like that presidential vote translates one-to-one into congressional vote, or that incumbency is distributed across the new districts in a way that doesn’t have consequences for your estimates. All to get at something you could easily test with an extension of the data you already have. Add in incumbency, run a model on some number of past years, and use those coefficients to predict for the new election.

    I’m not necessarily defending the approach we’ve taken at Monkey Cage in all its particulars. I’m sure there are aspects of it that could be done much better. But this just feels like you’re blindfolding yourself for no good reason.

    • Sam Wang

      Well, I do find your approach interesting, and it could be suitable if enough details are known. My initial read, however, is that there is a risk of large error bars – your previous posts indicated huge errors, larger than the observed scatter from 1946-2010.

      I wouldn’t call my approach blindfolding, so much as focusing on key parameters that capture the entire system. There is an uncertainty that results, but I believe it is the “right” uncertainty. We could probably have a good discussion of this in person.

      Getting errors right is a challenge. To quote the old saw, a theory should be as simple as possible, but no simpler. In principle, if I have reasoned this out tightly, you and I should be able to test of how much benefit is brought by the added parameters.

    • Eric McGhee

      Yes, there’s large error in our approach, and it seems almost entirely due to redistricting. But all we’re doing is reporting what we know and what we can’t know for certain given our model. I don’t see how you can get around that problem by just claiming to have the “right” uncertainty. Moreover, precision is of little use if your point estimate is radically biased. Nonetheless, I’m willing to let you have your point prediction and we’ll have ours.

      But this redistricting stuff seems a different kettle of fish. You’re talking about a counterfactual we’ll never observe directly, so the outcome of the election will tell us basically nothing about the quality of your estimate. The internal logic of the prediction becomes really key here, so I think you need to validate the assumptions you’re making with some data. The one-to-one presidential/congressional vote seems particularly problematic. Where does that assumption come from? If you add in an incumbency effect, you’re simultaneously assuming that the one-to-one translation does not occur.

      At the very least, I think you need to drop the error bars around these particular estimates. If you’re not going to base your assumptions in data, then you can’t realistically put error bars around it because you have no idea how large that error is.

    • Sam Wang

      I discussed all of this already if you care to read through. Unlike academic papers, the blog format is constrained by the cumulative nature of the activity. I might post a side thread on the right to dig into this more.

      Basically, I fit 1946-2010 overall-outcome data to seats = a0 +
      a1*vote +a2*lastcongressseats. a1 is the principal source of variation. a2 is much smaller, and contains history-dependent effects, one of which is called incumbency advantage by political scientists. All three coefficients have uncertainties, which can be propagated by standard means. This was described briefly in the second footnote in the House prediction that caused so much fuss.

      Very complex models in this area seem to be at risk of (a) unclear causal mechanisms, (b) double-counting of uncertainties, and (c) overfitting. In contrast, my argument can be laid out in a fairly simple fashion, and the error analysis is less burdened by these problems.

      I don’t know that I can get to this soon – it involves a certain amount of rewriting. But now that I sense you over my shoulder, I will have to attend to the details doubly.

    • Sam Wang

      All error bars came from analysis unless explicitly stated to be an assumption. Don’t tread on my blue suede error bars!

  • Jack Rems

    Eric McGhee’s point about the correspondence between presidential and downticket voting might be more germane to the forthcoming “incumbency effect” estimate than the gerrymandering effect, but it’s a very tangled web.

    I had seen some scary coverage in past years of computer-assisted gerrymandering. I imagine it has been a lot more effective with each decade, though even in the last round there were probably (I hope!) some faulty (“538”-style) assumptions. Does anyone here have access to any of the gerrymandering algorithms? (There’s also an interesting conflict between making a safe district for a particular politician and trying to maximize your party’s number of seats.)
    I hope your work here will build solid scientific evidence of how voters are systematically discounted; then maybe things will change.

  • Olav Grinde

    By controlling state legislatures, the GOP has been able to carry out redistricting. But more importantly, they have also been able to appoint secretary-of-states in all the swing states of which they won control in 2010. That means they’re in charge of purging voter rolls.

    Redistricting and changed voter rolls must be viewed in conjunction to get a true picture.

    Do we have state-by-state statistics on how many voters have been purged from the voter rolls?

    I have heard that for Colorado we are talking about 19 %. I can try to dig up a reference for that. But if true, this is astonishing, and together with redistricting changes the picture significantly.

    • Olav Grinde

      The reference is: Voter List Maintenance: Removal Actions. According to Greg Palast*, the numbers of voters scrubbed by the respective secretary-of-states include:

      Wyoming: 4.5 %
      South Dakota: 5.4 %
      Colorado: 19.4 %

      (* Billionaires & Ballot Bandits: How to steal an election in 9 easy steps, Greg Palast © 2012)

    • Sam Wang

      A source with somewhat better quality control is the Brennan Center for Justice. They recently reported that Colorado has abandoned its efforts.

      The Brennan Center documents voting rights in all 50 states, with a view toward protecting voters.

    • Olav Grinde

      Thank you. The Brennan Center for Justice writes:

      Last year Colorado Secretary of State Scott Gessler declared a virtual state of emergency — possibly 11,000 non-citizens on the Colorado voter rolls. Soon after, Secretary of State Ken Detzner in Florida upped the ante by claiming he had a list of 180,000 potential non-citizens.

      So let me see if I understand this correctly. Florida’s and Colorado’s secretary-of-states might have purged an astonishing number of “potential non-citizens” from their rolls, if they had not been stopped.

      Detzner and Gessler made a lot of noise about those numbers. In other states, officials have gone about their business more quietly.

      However, the Brennan Center addresses only two of 50 states. One cannot fail to wonder what may have happened in the others — below the radar of public awareness.

    • Sam Wang

      Here’s a key report from the Brennan Center. Also see this between Rachel Findley and me on voter ID laws.

    • Steve in Colorado

      What the SOS did was take everyone who didn’t use a mail-in ballot in 2010 off the permanent mail-in ballot list. Well, that was a low turnout election, so a lot of people who had been on the permanent mail-in ballot will now have to go to the polls in person- the probability of voting goes from 90% with mail in ballot to 60% without it.

    • MAT

      Or, to rephrase things – in Colorado, some people who would have in the past automatically received an absentee ballot, now will have to re-request one for this election (which is actually the norm in many states, including mine – you have to request absentee ballots for each election cycle). While I think maybe the filtering (one election) may have been a bit too strict, this doesn’t strike me as a totally unreasonable thing to do from an election boards standpoint. We too have tightening budgets, and mail costs money.

  • MAT


    It took me a few days, but I was able to discuss your previous voter purge question with our local director of elections. I’m in NC, so I can’t speak for other states, but… What I found out was that if someone shows up to vote who has been previously registered but has been purged, then what happens next depends on the circumstances. If, for example, they lost voting rights due to committing a felony, if they can show that they have regained rights by completing the sentence, we’ll restore them. If it can be shown that the purge was simply in error, we’ll restore them. If due to information we’ve received that they had moved out of our jurisdiction which is incorrect, with proof of residency, we’ll fix it. If purged because we think they are dead ( and yes, this does happen), we’ll reactivate the registration. If none of the above, you still have the right to vote provisionally and your circumstances will be addressed.

    One thing I would caution about is the difference between voter registrations being ‘inactivated’ vs an actual purge. If someone has not voted in two straight general elections, we will send a multitude of letters to the registration address asking the voter to verify that they still live there. If no response, then the registration would be inactivated. But the act of showing up to vote and a verification of who you are and where you live is sufficient to turn the registration back on, and is usually accomplished on the spot. I’m wondering if perhaps the scary type numbers you are hearing are deactivations, which are common, vs actual purges.

    Most purges of registrations occur when either the voters have changed registrations to another jurisdiction and we get notified because of a changed registration or we are notified by an agency like the DMV or another government entity that the voter no longer resides in our county. It’s not a perfect system, so the process is always to allow the vote, even if by provisional ballot, so that the individual circumstances can be investigated.

    • Olav Grinde

      MAT, thank you for responding!

      The book by Greg Palast, which I found fascinating, was also an exercise in frustration. He does not provide the footnotes that I would expect. Gradually I found it necessary to take what he had to say with a good fistful of salt. While the BBC reporter and author does make some interesting points, I suspect his numbers are significantly exaggerated. It’s quite possible that Palast confuses “purged” with “inactivated”.

      For some time I have been trying to find actual numbers for the voter purges carried out recently and in the last two years.

      I must confess that I have not had success. If there is a state-by-state overview, which there surely must be, then I have not been able to find it.

      It would be good to be able to quantify this, so we know what we’re actually dealing with.

    • Olav Grinde

      Yes, I have been following that site closely, ever since you pointed to it in an earlier post. Hasen’s site is excellent!

    • Matt McIrvin

      It varies from state to state. In MA, while there haven’t been big purges, it’s surprisingly easy to get inactivated by forgetting to send in a form, even if you vote in every election. I got on the inactive list between the presidential primary in the spring and the state primary in September, both of which I voted in.

  • securecare

    When the election is over and the “smoke” clears it might be useful for future elections to have a consolidated list of these credible sites that come up in discussion.

    Yep, one more thing on a long list of things to do while demands of ones career pile up.

    Great job here by all concerned, thanks to all.

  • Joel

    Big shift in the meta-margin today. Would fit the debate narrative, although checking pollster, I notice that the ACU pollster dumped a lot of state polls today. Wondering if that’s causing the majority of the effects.

  • Olav Grinde

    A naïve question, if I may:
    Why have voter rolls at all?

    Why not have a system whereby all residents who are citizens are automatically eligible to vote, without having to register?

    • MAT


      Jurisdiction. Registering is mainly a way to determine for what and who you are entitled to vote. If we don’t know where you live, we don’t know if you are eligible to vote on that sewer bond referendum that is on the ballot for one precinct, but not the other.

    • Matt McIrvin

      That said, registration could be much more automatic than it is, since local governments have many ways of tracking who is in their jurisdiction.

      The regulations that make it most difficult to register and easiest to get disenfranchised tend to be a legacy of Jim Crow regimes. I think it’s significant that the states that have things like easy same-day registration (or no formal registration at all) have a tendency to be extremely white states in the northernmost tier of the country.

  • Olav Grinde

    @MAT & Olov: Ah, silly me! That of course is an answer, but only partly. I read the first part of that paper, Olov, and looking forward to reading the rest. I see it’s not as long as it first appears, since about half of it is footnotes. ;)

    Matt: I agree. When the dust settles, it would be very interesting with a geographic comparison between voter ID laws, voter purges, alarming local/demographic peaks in voters compelled to cast provisional votes, “technical glitches” etc.

    California seems to be leading the way: simple online registration, and Election Day registration laws. Perhaps a model that far more states should adopt?

  • Ken O'Brien

    Is there a URL link to a similar analysis to see if the electoral college at presidential level makes a popular vote/electoral vote winner mismatch more likely for Obama versus Romney in this election?

    • Matt McIrvin

      The PV/EV split is one of the things Nate Silver tries to calculate, for what it’s worth: he currently has the chance of it happening either way at a few percent, with Obama somewhat more likely to benefit than Romney.

    • Ken O'Brien

      Thanks. That does seem small. In comparison, I read Dr. Wang’s 1.8+/-1.0% House (R) advantage to say that if popular vote splits exactly even, there would be an ~90% change (R)’s would still win the House.

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