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From an AP article titled Analysis indicates partisan gerrymandering has benefited GOP:

The AP’s findings are similar to recent ones from the Brennan Center for Justice at the New York University School of Law, which used three statistical tests to analyze the 2012-2016 congressional elections. Its report found a persistent Republican advantage and “clear evidence that aggressive gerrymandering is distorting the nation’s congressional maps,” posing a “threat to democracy.” The Brennan Center did not analyze state legislative elections.

[...]

For Democrats to complain of gerrymandering is “pure nonsense,” said Matt Walter, the Republican committee’s president.

Are the Republicans correct when they say that gerrymandering has little effect or does it have a significant effect? If so, how strong does the effect happen to be?

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Background

This bears some confusion. Gerrymandering is a real thing, but it is not the primary problem with (from the other answer)

Regardless of which side is doing it, a portion of the population is not getting a fair representation and that's (again in my opinion) a problem.

The number one reason why people lack representation in the United States is always going to be the winner-take-all system. Each congressional district elects one Representative, and those who did not vote for that candidate do not get representation of their choice. This disenfranchises up to half of the population in each district. I.e. urban Republicans and rural Democrats do not get representation.

The efficiency gap is looked at on a group basis, mostly per state because that is where redistricting occurs. It measures how many votes are wasted or lost because they either take the vote above 50% for the winner or are votes for the loser. So there will be an efficiency loss of 50% for every district, split between the two parties (efficiency gap analysis ignores others).

At the national level it could be argued that the gerrymandering might be even itself out to some degree (not sure if that's the case or not - from the numbers I've seen it appears that the GOP has an advantage) but in my opinion two wrongs don't make a right.

Efficiency gap analysis doesn't measure that. In fact, it does the exact opposite. It says that if one side is benefiting more than the other side, that we should transfer some of that benefit to the other side. This doesn't change the amount of disenfranchisement. It just moves it from one side to the other. Because that eliminates the gap in the efficiency. I.e. it is all about making the wrongs even. It makes no attempt whatsoever to remove the wrongs.

Worse, efficiency gap analysis encourages the introduction of wrongs. Normal redistricting might put an entire county in the same district while efficiency gap analysis encourages breaking up cities and counties to produce "fairer" districts.

From a comment:

Democratic votes being concentrated in cities doesn't matter for gerrymandering. It isn't a problem to have a lot of geographically small districts inside a city, while having a small number of very geographically large districts in rural areas. In other words, you can make the districts "fair" even given the demographics.

The normal problem with urban vs. rural districts for gerrymandering is that urban districts are more Democrat (have a higher efficiency loss for one party) than rural districts are Republican. This is why efficiency gap analysis is promoted by Democrats as a measure of gerrymandering. It promotes their goals of more Democratic districts with very little loss of districts to the Republicans.

Look at states like Massachusetts and Connecticut for example. In both states, the congressional delegation is entirely Democratic. But in both states there is a large enough Republican minority that they occasionally win the governorship. In Massachusetts, the breakdown is roughly 50% Democrat, 25% Republican, and 25% other. So in a proportional system, the Democrats should have four to five seats while the Republicans and other each have two to three seats. As is, Republicans and other have zero seats. In fact, nationally, other has zero seats in the House of Representatives.

Efficiency gap analysis doesn't help with that. In fact, in a state with 75% or more of voters in one party, efficiency gap analysis says that the majority party should get 100% of the seats. The disenfranchised 25%? Not their problem. Same thing with those not in the two major parties.

Source: Partisan Gerrymandering and the Efficiency Gap (PDF), Nicholas 0. Stephanopoulos & Eric M. McGhee

Gerrymandering

Election analyst Sean Trende of Real Clear Politics did an analysis of gerrymandering where he measured the increase in partisanship. He found

If we define “Highly Partisan Districts” as those that are four points or more Republican (or Democratic) than the country as a whole, there were 195 such districts in 2010, and 200 in 2012. In 2000, under the previous set of lines, there were 193 “highly partisan” Republican districts.

So Republicans added five "Highly Partisan Districts" during the redistricting cycle of 2010-2012. And seven if we count from 2000 (which includes two redistricting cycles. This is noteworthy because prior to that, it was Democrats who controlled redistricting in most states. It's only the last couple censuses where Republicans have been able to gerrymander more than Democrats.

The Washington Post Redistricting Scorecard used to show the same five seat advantage for Republicans in the last redistricting.

It's worth noting that both of these include North Carolina. Why is that important? Democrats controlled the state legislature and governorship in North Carolina in 2001 when the last redistricting had been done. And they gerrymandered the heck out of it. So about half the gains in North Carolina in 2012 were not from the introduction of a Republican gerrymander but from the elimination of the Democratic gerrymander.

Fair Vote analyzed the North Carolina districts. They have a plan to combine districts into superdistricts with three to five seats in each. Under that analysis, they found that North Carolina should have a slight Republican lead but that Democrats should be able to win 7-6 in a good year while Republicans could win up to 8-5. The average result would be a 7-6 victory for the Republicans.

Note that the actual results swung from 8-5 Democrat to 10-3 Republican. This accounts for the entire improvement from 2010 to 2012 among Republicans, all five seats. Yet half of this was the elimination of the previous Democratic gerrymander. If we knock off two seats, the Republicans would have only gained by three seats by gerrymander. The other two being gained from the elimination of a gerrymander.

An analysis on Politics.SE found that under Cook Partisan Voting Index, Republicans did better than their national average in just three more districts in 2008/2012 versus 2004/2008.

TL;DR: Republicans gained three to five seats in the 2011 redistricting. depending on how one measures.

  • This answer is poor regarding redistricting per se, because of the focus on highly-partisan districts. If you have two neighboring districts with 100 people each, one with (53 D, 47 R), and the other with (49 D, 51 R) you might be able to redistrict the two so that you get (51 D, 49 R) in both of them. So you've made a small change in the ratio of D to R, and you've kept the overall sizes in population and maybe even in area. You may not even have drawn the district lines to be crazy. And still you got to win 2 districts for D (just an example - you can switch it the other way around). – einpoklum Dec 24 '17 at 13:50
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    @einpoklum Right, producing two D+2 districts by Democratic gerrymandering, which would have produced two Republican seats. Because the Republicans are winning most D+2 seats or better. That's a bit misleading in that the usual argument is that it is Republican gerrymandering that benefits Republicans, not bad Democratic gerrymanders. The purpose of this answer is not to explain gerrymandering. Skeptics is the wrong place for that. It's to debunk the bad claims made about efficiency gap analysis, which fails in highly partisan districts. If you have questions, Politics.SE is better. – Brythan Dec 24 '17 at 15:24
  • Skewed vote total/seat count does not have to be Gerrymandering. In Winner Take All a.k.a. First Past The Post voting, that is sometimes called a "wasted vote" effect. Here in British Columbia, Canada, we are currently having a referendum on weather to keep our First Past The Post system or switch to proportional representation. elections.bc.ca/referendum/about-the-referendum/… For instance our last election had disproportionate results but Gerrymandering isn't widely cited as the cause: en.wikipedia.org/wiki/British_Columbia_general_election,_2017 – rusl Nov 17 '18 at 1:23
  • A significant reason people lack representation in the United States is because the congressional districts are massive, averaging over 650,000 people each. You could keep winner-take-all and double or triple (or more) the number of representatives/districts and representation would be much better than if you kept the number of districts the same but changed how their representatives were elected. – kbolino Jan 8 at 0:34
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Both parties are guilty of gerrymandering. Most notably, Maryland has been gerrymandered to benefit the Democrats and North Carolina for the Republicans - widely considered the 2 worst gerrymandered states.

However, it is possible that one party has a bigger gerrymandering advantage than the other.

The Washington Post has a great article on the topic. To summarize:

This election year we can expect to hear a lot about Congressional district gerrymandering, which is when political parties redraw district boundaries to give themselves an electoral advantage.

... the point of gerrymandering isn't to draw yourself a collection of overwhelmingly safe seats. Rather, it's to give your opponents a small number of safe seats, while drawing yourself a larger number of seats that are not quite as safe, but that you can expect to win comfortably.

The author claims that his research has shown that

...the Democrats are under-represented by about 18 seats in the House, relative to their vote share in the 2012 election.

This is collaborated by the Brenner Center for Justice

Using data from the 2012, 2014, and 2016 election cycles, Extreme Maps finds that partisan bias resulting largely from the worst gerrymandering abuses in just a few battleground states provides Republicans a durable advantage of 16-17 seats in the current Congress...

How is that measured? Nicholas O. Stephanopoulos and Eric M. McGhee's article "Partisan Gerrymandering and the Efficiency Gap" describes how to measure the degree of gerrymandering. It's fairly simple, basically, you expect the number of seats each party gets to be fairly proportional to the amount of votes it received. A 40-60 vote split resulting in 60-40 seat split obviously indicate that outside factors are at work.

Another Washington Post article that illustrates how gerrymandering works claims that in Wisconsin, the gerrymandering gives the GOP 10% advantage.

Wisconsin gerrymandering graph

While it's only one state, I think that's significant for the residents of that state. At the national level it could be argued that the gerrymandering might be even itself out to some degree (not sure if that's the case or not - from the numbers I've seen it appears that the GOP has an advantage) but in my opinion two wrongs don't make a right. Regardless of which side is doing it, a portion of the population is not getting a fair representation and that's (again in my opinion) a problem.

  • Regarding claims about underrepresentation at the national level, the relevant statistics may be skewed by Washington and California's use of a top-two "jungle" primary system. California especially leans heavily to the Democrats, which makes it fairly common for the winners of the primary election to both be Democrats. The end result is 100% of a district's votes going to the same party, since non-voters are not counted. Thus, a Republican voting for a Democrat because there is no other choice would add to the appearance that Democrats are underrepresented nationally. – kbolino Jan 8 at 0:31
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"Evaluating partisan gains from Congressional gerrymandering: Using computer simulations to estimate the effect of gerrymandering in the U.S. House" by Jowei Chen, David Cottrell

was the paper that evaluated this.

Abstract:

What is the effect of gerrymandering on the partisan outcomes of United States Congressional elections?
A major challenge to answering this question is in determining the outcomes that would have resulted in the absence of gerrymandering. Since we only observe Congressional elections where the districts have potentially been gerrymandered, we lack a non-gerrymandered counterfactual that would allow us to isolate its true effect. To overcome this challenge, we conduct computer simulations of the districting process to redraw the boundaries of Congressional districts without partisan intent. By estimating the outcomes of these non-gerrymandered districts, we are able to establish the non-gerrymandered counterfactual against which the actual outcomes can be compared.
The analysis reveals that while Republican and Democratic gerrymandering affects the partisan outcomes of Congressional elections in some states, the net effect across the states is modest, creating no more than one new Republican seat in Congress.
Therefore, the partisan composition of Congress can mostly be explained by non-partisan districting, suggesting that much of the electoral bias in Congressional elections is caused by factors other than partisan intent in the districting process

Recent 538 Gerrymandering podcast made a similar claim (most of the results have little to do with partisan gerrymandering) but I don't think they made any quantitative claims, I need to find the podcast transcript.

  • Can you link the podcast towards which you are referring? – Christian Dec 22 '17 at 14:25
  • @Christian - they covered the topic in several different ones; last one was in specialized "The gerrymandering project" one. – user5341 Dec 22 '17 at 14:40
  • Can you add a link to the one you meant in your answer? – Christian Dec 22 '17 at 14:41
  • @Christian - fivethirtyeight.com/tag/gerrymandering-podcast – user5341 Dec 22 '17 at 15:04

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