Gerrymanders, Part 2: How many voters were disenfranchised?

January 2, 2013 by Sam Wang

(Welcome, redditors! And for the hardcore nerds…)

Redistricting is a large and sometimes arcane subject. Take a look at the comments section for the last post. Some of you are quite knowledgeable on the subject. Others are new to it. Before I continue, I’ll lay out some basics, and explain what it is about this problem that interests me.

In the US system, the House of Representatives is elected on the basis of districts. State boundaries are fixed, and the number of Representatives in each state is determined after the Census, which occurs every 10 years. It is left to each state how to elect its Representatives. The current standard practice is that somebody draws up districts, each of which then elects one Representative. A similar procedure is used to determine state-legislature districts.

In such a system, one issue is how to represent the interests of subgroups such as political parties and ethnic minorities. If a minority is small, they can end up on the losing side of every election. Indeed, a general principle of the current district system is that a given fraction of the vote below 50% will usually lead to a fraction of the seats much smaller than 50%. One solution is to craft districts that cluster groups with shared interests, as was recently done in New York state. Another solution advocated by several commenters was that of multi-member districts. Overall, the topic is one of  “good government,” which is worthwhile…but not my focus. I do not think it is the central crisis. For purposes of the analysis I have been doing, then, I am using the current standard district system, as practiced across the nation, as a reference for “fairness.”

I also won’t delve too far into structural challenges that arise from the fact that dense populations tilt Democratic, while sparse populations tilt Republican. It is worth understanding what is baked into the system, and has been analyzed by John Sides and others. To the extent that there is an action item, it is in the “good government” category: redistricters of good will could address it wisely if they chose to.

Which brings us to the topic I do care about: “bad government.” My goal is to identify actions that purposely separate the legislative process from overall popular will. It can also happen when redistricting is under the control of partisan legislators, who can (and do) protect incumbents or an entire political party. In the extreme, fewer than 50% of voters can elect more than 50% of the Representatives. In addition, the construction of polarized districts can leave policy positions at the mercy of primary voters.

In Part 1, I laid out a state-level measure of partisan gerrymandering: the number of seats by which a delegation differs from a “typical” national outcome. Here it is, applied to all 50 states.

This is calculated using the vote outcomes of non-extreme states (shaded in gray) to feed the simulations. Red shading indicates Republican Party control over redistricting, blue indicates Democratic Party control, and black indicates nonpartisan commission (AZ) or a court-ordered map (TX).

(I should say that using nongerrymandered districts for the simulations only increases the importance of the “what-if” scenario. Repairing the red-state gerrymandering would lead to a swing of 30-34 seats toward Democrats; repairing the blue state of Illinois would lead to a swing of 2-4 seats toward Republicans.

Finally, applying the gray-states rules to all states would give a mean outcome of 215 D, 220 R, with some variability. That’s compared with the House margin of control starting Thursday, a 33-seat margin of 234 R, 201 D. So if the outlier states had been districted according to prevailing standards, a switch in control this year would have been within reach. At a minimum, power would be more evenly balanced and the possibility of paralysis reduced.

It is safe to say that these outcomes did not arise by chance. Out of 10 states with extreme outcomes, 8 favored the party that controlled the process, and two were under the control of a nonpartisan commission. Indeed, the extreme cases closely match a redistricting watchlist published by the Washington Post in March 2011. From that list, only Nevada and New York have escaped this Hall of Shame.

In the case of the commission-drawn and court-ordered maps, it is possible to see why the Arizona GOP would be displeased. They also didn’t like the fact that there were too many competitive districts, which is usually a good-government goal. Texas is interesting because the redistricting was court-ordered, post-Tom DeLay. 60% of Texas voters voted for Republicans to elect 24 out of 36 seats, which sounds like a lot but is a substantial underperformance.

Now let’s estimate how many voters were disenfranchised by looking at the simulation results:

In the seven Republican-controlled states, the total votes cast were 16.22 million (50.8%) for Republicans, 15.68 million (49.2%) for Democrats for a 74 R, 32 D outcome. The simulations indicate that this seat split would normally only require 11.7 million Democratic votes. In other words, 4 million Democratic voters in seven states were disenfranchised.

In Illinois, the total votes cast were 2.74 million (55.4%) for Democrats, 2.21 million (44.6%) for Republicans for a 12 D, 6 R outcome. In this case, 1.8 million Republican votes would have been “enough” to elect this delegation, so that about 400,000 Illinois Republican voters were disenfranchised.

Therefore the disenfranchisement due to partisan-controlled redistricting was a total of 4.4 million voters from both parties. Democrats  were disenfranchised more than Republicans, at a ratio of 10:1.

I will conclude by saying that the problem of partisan gerrymandering has been identified as a major problem, both by nonpartisan Congressional scholars Mann and Ornstein (in book and column), and recently by partisan commenter David Atkins. The problem is finding a remedy. Republicans had an extremely lucky year in 2010, when they assumed control of a record number of legislatures – and therefore control over redistricting.

At this point, remedies would fall in the following general categories:

  1. Persuading courts of the degree of disenfranchisement;
  2. Resolving issues at the ballot box; and
  3. Improvements in the future redistricting process.

This all gets into the question of how to fix “bad government.” That’s a big topic. One starting point would be the California example.


Robert Slaven says:

Thanks for your analyses! Gerrymandering strikes me as the second-biggest stumbling-block to real democracy in America (#1 being campaign financing etc.). I’m trying to do some amateur analysis of my own re: gerrymandering, but I’m having trouble finding good data; is there a single site that has easy-to-download data for all states’ Congressional races?

Jon Denn says:

I’ve been studying electoral form diligently for a couple years now. This work is fascinating but it is rather a band aid on a festering wound. The wound is caused by Single Mark Ballots. Oversimplifying, because of vote splitting, it assures a duopoly. And actually given this information and demographic shifts especially in Texas—a coming monopoly. Both are awful for a democratic republic. Here is a link to drill down on Banning Single Mark Ballots by DEMRA the Declaration of Electoral Methods Reform Activists. I have come to the conclusion that no meaningful electoral reform of any aspect will be significant until a firm foundation is built through better balloting.

Sam Wang says:

In the context of the current problems, I am concerned that this is a bit of a good-government pipe dream. If we returned to a status quo ante, circa 1990 or earlier, we could entertain the idea. In the meantime, it doesn’t seem like where the biggest antidemocratic difficulties lie at the moment – at least not the ones that can be addressed. My two cents.

wheeler's cat says:

A presidential system is a two-party system. If the founders had given us a parliamentary system by design, then there could be more viable parties.

Jon Denn says:

Enacting anti-gerrymandering legislation is certainly a very difficult task, so is abandoning antiquated voting technology. My point is Anti-Gerrymandering is a great grievance. It however doesn’t have any salient solution that doesn’t result in either maintaining a duopoly or the unintended consequence of a monopoly. One party rule doesn’t seem to be a pathway to end crony capitalism, or achieving No Political Party Should Be Privileged, or stopping elected officials from taking money from corporations they regulate, or the two parties controlling the debates, etc. This results in the oligarchs and plutocrats having all the power, and makes voting almost irrelevant: as evidenced by the disenfranchised who have just given up voting. They feel the system is rigged—and they’re mostly correct. There are WAY more total disenfranchised by the entire system than by gerrymandered districts.

Felix says:

Great analysis as always! However I wonder what the basis is for calling states shaded in gray “non-extreme”? Maybe the non-partisan redistricting in AZ and TX are setting the non-extreme numbers? Could this indicate that conservative ‘bad government’ has been going on for a lot longer than we would wish to believe….?

Steve Withers says:

Most democratic countries (over 80%) avoid gerrymandering entirely by using proportional voting system that allocate seats based on the share of the party vote. For example, 10% of the vote would win a party 10% of the seats. It doesn’t matter where a voter lives…their vote will always count to representation by the party they support. Such systems also deliver multi-party legislatures….giving voters real power to hold entire parties to account….not just one person. Virtually all new democracies adopt proportionality. Only a relative handful still operate non-proportional voting system. See – Americans educating about and promoting proportional elections.

Sam Wang says:

To reiterate, this is not a real solution. There is no clear political route to passing it in states where redistricting is causing the problems. To revive an earlier promise, if something like this ever passes in any of those eight problem states, I will eat a bug.
For those who are new here, this site focuses on topic areas where action is likely to lead to an improved outcome. Thumbsuckers beware!

Diane Trefethen says:

While it is debatable as to how much power States have to set the rules for State elections, the federal government does have final say. Article I, Section 4 of the Constitution grants States the authority to write election laws but also states “Congress may at any time by Law make or alter such Regulations, except as to the Place of chusing Senators.” So if a Federal law were passed which required House members to be chosen by proportional representation, then that would be the law of the land and supersede state laws mandating otherwise.

wheeler's cat says:

umm well….i was actually serious about that projective geometry/computational geometry stuff. maybe districts could be forbidden from violating the definition of a convex hull. that would stop the salamander effect. maybe the whole state could be segmented into convex hulls that were demographic fractals of the state itself.

wheeler's cat says:

maybe its more of a tiling problem. i don’t know how districts are originally set up, but i imagine they are sort of natural fractal convex hulls that get tweaked by census data and changing of party control.
maybe something like this could work.

Amitabh Lath says:

In Fig 1, how is “neutral outcome” defined? Is it a linear regression fit on the distribution of the simulations?
Also, what is the mean and sigma of Fig 1? Are PA, OH > 5 sigma away? (sure looks it).

Sam Wang says:

Neutral outcome is defined as a discrepancy of <1.2 seats from the mean simulated outcome as described in Part 1. The mean is -0.20 seats and the SD is 1.09 seats.

Some Body says:

Question (related to both posts): Could doing your calculation with 2010 district results (shifted by a constant to reflect the change in popular vote in each state between 2010 and 2012) as the pool of data to select from, instead of the actual 2012 results, allow the result also to reflect the baseline you calculated before?
I’m not sure I’m making myself clear, and the math required is beyond me, but it just struck me as a possibly interesting idea to explore.

Sam Wang says:

Yes, that’s why I want the 2010 results. Also earlier results. The prediction would be that the discrepancy would show a sudden step at 2010.
Your question illustrates the power of designing an analysis with sharp time resolution, which is what I have attempted to do here.

Mike Clinch says:

Figure 1 is a little biased towards the central distribution by the inclusion of the seven states where there is only one representative per state. While Republicans have a small advantage in these seven states (5 red states – Alaska, Montana, Wyoming, North Dakota and South Dakota, vs. 2 blue states – vermont and Delaware), the deviation from the ideal distribution is less than 0.5 representatives in these seven states. Removing them would make the tails caused by gerrymandering stand out a little more.

Sam Wang says:

That’s good. Thank you!
After omitting the at-large states from both the sampled districts and the calculation of outliers, the answer to Amit Lath’s question is now a mean of -0.22 seats and an SD of 1.19 seats. So “neutral outcome” turns out to be defined as within +/-1.0 SD.
The histogram (all 50 states) looks like this now:

Olav Grinde says:

So here is an alarming question…
The GOP has suggested changing the rules for selection of Electoral College Votes in states in which they control the state legislatures. Rather than winner-takes-all, they’re talking about district-by-district elections. In other words, the gerrymandering would have profound implications also for the Presidential Election!
My question is this:
If the rules had already been changed in those swing states in which the Republican Party controls the state legislatures, might Mitt Romney have been elected President instead?
How profound is the danger to future Presidential Elections?

Olav Grinde says:

As I understand it, under the new rules, Romney would have won a significant majority of Pennsylvania’s Electoral College votes — and that’s just one state.
I have not yet, however, seen a complete analysis.

Sam Wang says:

Current information from @Redistrict (David Wasserman) has the district-wise count at Romney 225, Obama 206, 4 to be determined. This was previously covered here. This would effectively put Presidential politics in the hands of state redistricters. It’s a step backward from the current Electoral College.

MAT says:

Complicating Olav’s question are cases where proportional EC votes vs winner talk all would have cost Romney, such as in NC.
Anyone have a good source of presidential results broken down by congressional district? It would be interesting to test Olav’s question, then look at how what Sam is illustrating would map out onto presidential elections.

Olav Grinde says:

Thanks, Sam.
MAT, but the whole point Republican Party would only pass proportional EC rules where it is to their advantage!
I really cannot see a Democratic-controlled legislature in North Carolina passing proportional rules in order to yield a Blue advantage.

Sam Wang says:

Agreed. It bears mentioning that the asymmetry I am describing indicates a scorched-earth strategy by one side only. That should affect any armchair suggestions on what to do!

MAT says:

Better late than never, I hope:
Here is how the counts would have changed (i.e. take these away from 332 if each of the following states changed to award by congressional district). I added the 2 at large electors to whoever got the most congressional districts:
Colorado: -3
Florida: -18
Iowa: -1
Michigan: -11
Nevada: -1
Ohio: -14
Penn: -15
Virginia: -9
Wisconsin: -7
That’s a swing of 80 electorial college votes, Obama won by 72. I haven’t yetlooked at which of the above states have full republican control of legislatures and governor, but basically, yes, a scorched earth approach could change elections substantially.

Dave Kliman says:

a great way to understand gerrymandering is to play the game here:
by the time you have mastered the game, you will discover that it is not people who elect representatives, but these so called representatives who decide who the people will be able to elect.

D D says:

I believe our districts in Texas were drawn by the legislature first and then during the litigation Texas Federal judges found in favor of the plaintiffs redrawing the maps. The AG appealed and when it was all said and done the 5th circuit ordered the district judges to redraw the districts in conformity with their ruling. This couldn’t be donenbefore the November elections so back we went to the legislative drawn districts. The judges will draw new districts I think by April 2013. For now Austin is 5 districts disenfranchising around 500,000 people.
The pres clearance was avoided by the AG and is part of the case pending in the US Supreme Court regarding constitutionality of Section 5 of the Voting Rights Act.
In the end I would say there should be 3 to 4 additional Democratic districts if fairly drawn.
As I am sure you know the 5 counties with the largest cities went for President Obama, but with a total of 254 counties a 60/40 split would be ok because 2020 will really be ugly for the GOP. Population of Hispanics, Afro Americans, women and the “highly educated elite ” will be a majority coalition no gerrymandered districts can overcome. This assumes Section 5 survives.

Olav Grinde says:

On a side note: Barney Frank is willing to do a job in the Senate on behalf of Massachusetts, albeit temporarily. God knows he’s needed!

Amitabh Lath says:

The corrected distribution after Mike Clinch’s comment looks really non-gaussian now.
Basically a spike by zero, plus a linear. There isn’t any point in estimating a FWHM for the core distribution or anything fancy. PA and OH are really outliers now, something went wrong there.
In these two states, would GOTV efforts help? It’s been said that D voters do not turn out for off-year election (or state elections w/out gov on ballot).
So let’s hope the 2012 coalition that elected Obama keeps voting even in the midterms.
Are there any R districts in PA or OH that would have been close or flipped if 2010 turnout had been like 2012 turnout? How “safe” are these safe R districts?

Jon Denn says:

I’m on the board of a nonprofit that will be announcing the Clean Government Alliance with well know national chairs on the far left and far right, and probably center, left and right. The purpose is to draft a Constitutional Amendment for omnibus electoral reform. If you have language or methods you would like included for anti-gerrymandering or fair redistricting please let me know ASAP.

Olav Grinde says:

That’s very interesting!
First of all, I would be very interested in knowing what thoughts you yourself have. Do you, for instance, believe such an amendment should address campaign funding, PACs, SuperPacs, transparency of campaign contributions?
One thing that I would like to see is automatic voter registration — if you’re a US citizen and reside in a particular state/district, then you are automatically registered to vote.
This would go a long way toward almost eliminating “provisional votes”.
Also, such an amendment should address the re-enfranchisement of persons who have served their prison time.
One key point (perhaps first and foremost): the constitutional amendment should require a verifiable and auditable paper trail in all elections.

bluemeanies says:

I wonder if the Texas map seems to lean more Dem because many Texas districts suffer from uncontested R seats. Weak, innactive local Dem committees fail to nominate a House candidate and thus the Dem votes in those districts are invisible, tilting the statewide numbers R. I think there were 40 R uncontesteds (by D) nationwide and in TX we have TX-3, TX-13, TX-17, TX-19 (5 seats) with only TX-29 the other way around. Just a thought, might be nothing.

C harles Slaka says:

If Gerrymandering is looked at in the context republicans two goals which can be accomplished.
1. The first to create an artificial district that more often than not exclude the segment of voters that would normally be represented.
As it was mentioned, both parties have used this reprehensible practice. BUT republicans have another
2. The voters that are being excluded are infact being excluded.
Republicans know if they district most of the population in as an example 3 out of 10 districts.
the total population of 10 districts is 1 million.
750000 voters almost all democrats who vote is from 3 districts.
THE REMAINING 7 DISTRICTS consist of 250000 voters, predominately republicans.
Even if 750000 voters vote democrat, the electoral votes will be awarded to a republican with 25 percent of the vote.
IN ESSENCE, 750000 VOTERS WILL BE DISENFRANCHISED, that is their vote count.

Waren D. Smith says:
discusses “shortest splitline algorithm” for redistricting. More detailed examination here:

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