Republicans will likely keep their House majority – even if Clinton wins by a landslide – and it’s because of gerrymandering.

By Michael Latner

While the presidential race has tightened, the possibility of Donald Trump being defeated by a wide margin has some Republicans worried about their odds of retaining control of Congress. However, only a handful of Republican-controlled districts are vulnerable. Speaker Paul Ryan’s job security and continuing GOP control of the House is almost assured, even if Democrats win a majority of the national Congressional vote. How is it that the chamber supposedly responsive to “The People Alone” can be so insulated from popular sentiment? It is well known that the Republican Party has a competitive advantage in the House because they win more seats by narrow margins, and thus have more efficiently distributed voters. What is poorly understood is how the current level of observed bias favoring the GOP was the result of political choices made by those drawing district boundaries.

This is a controversial claim, one that is commonly challenged. However, in Gerrymandering in America: The House of Representatives, the Supreme Court, and the Future of Popular Sovereignty, a new book co-authored by Anthony J. McGann, Charles Anthony Smith, Alex Keena and myself, we test several alternative explanations of partisan bias and show that, contrary to much professional wisdom, the bias that insulates the GOP House Majority is not a “natural” result of demographic sorting or the creation of “majority-minority” districts in compliance with the Voting Rights Act of 1965. It is the result of unrestrained partisan gerrymandering that occurred after the 2010 Census, and in the wake of the Supreme Court’s 2004 decision in Vieth v Jubelirer, which removed legal disincentives for parties to maximize partisan advantage in the redistricting process.

Partisan bias tripled after congressional redistricting

We measure partisan bias using the symmetry standard, which asks: What if the two parties both received the same share of the vote under a given statewide districting plan? Would they get the same share of seats? If not, which party would have an advantage?

We calculate seats/votes functions on the assumption of uniform partisan swing – if a party gains 5% nationally, it gains 5% in every district, give or take an allowance for local factors (simulated through random effects that reduce our estimates of bias). Linear regressions provide an estimate of what level of support the Democrats expect to win in each district if they win 50% of the national vote, given the national level of support for the party in actual elections, and we generate a thousand simulated elections with hypothetical vote swings and different random local effects for each district, to create our seats/votes functions.

Figure 1: Seats/Votes function for Congress 2002-2010
SV2010//embedr.flickr.com/assets/client-code.js

Figure 2: Seats/Votes function for Congress 2012
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Figures 1 and 2 show the seats/votes functions under the 2002-2010 Congressional districts, and the 2012 post-redistricting districts, respectively. We observe a 3.4% asymmetry in favor of Republicans under the older districts. This is still statistically significant, but it is only about a third of the 9.39% asymmetry we observe in 2012. Graphically, the seats/votes function in Figure 1 comes far closer to the 50%votes/50%seats point. The bias at 50% of the vote is less than 2% under the older state districting plans, compared to 5% in 2012. That is, if the two parties win an equal number of votes, the Republicans will win 55% of House seats. Furthermore, the Democrats would have to win about 55% of the vote to have a 50/50 chance of winning control of the House in 2016. Thus it is not impossible that the Democrats will regain control of the House, but it would take a performance similar to or better than 2008, when multiple factors were favorably aligned for the Democrats.

Increased bias did not result from “The Big Sort” 

Perhaps the most popular explanation for increased partisan bias comes from the “Big Sort” hypothesis, which holds that liberals and conservatives have migrated to areas dominated by people with similar views. Specifically, because Democrats tend to be highly concentrated in urban areas, it is argued, Democratic candidates tend to win urban districts by large margins and “waste” their votes, leaving the Republicans to win more districts by lower margins.

The question we need to consider is whether the concentration of Democratic voters has changed relative to that of Republican voters since the previous districts were in place. In particular, if it is the case that urban concentration causes partisan bias, then we would expect to find relative Democratic concentration increasing in those states where partisan bias increases. In order to address this question, we measure the concentration of Democratic voters relative to that of Republicans with the Pearson moment coefficient of skewness, using county-level data from the 2004 and 2012 presidential elections. As shown in Table 1, in most states the level of skewness toward the Democrats actually decreased in 2012.

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In twenty-seven out of the thirty-eight states with at least three districts, the relative concentration of Democratic voters compared to Republican voters declines. Moreover, in those states where partisan bias increased between the 2000 and 2010 districting rounds, those with an increase in skewness are outnumbered by those where there was no increase in skewness, by more than two to one. We also find that there was reduced skewness in most of the states where there was statistically significant partisan bias in 2012.

Of course, we should not conclude that geographical concentration does not make it easier to produce partisan bias. North Carolina was able to produce a highly biased plan without the benefit of a skewed distribution of counties, but to achieve this, the state Generally Assembly had to draw some extremely oddly shaped districts. While the urban concentration of Democratic voters makes producing districting plans biased toward the Republicans slightly easier, it makes producing pro-Democratic gerrymanders very hard. In Illinois, the Democratic-controlled state legislature drew some extremely non-compact districts but still only managed to produce a plan that was approximately unbiased between the parties.

Increasing racial diversity does not require partisan bias

Another “natural” explanation for partisan bias, one that is especially popular among Southern GOP legislators, is that that it is impossible to draw districts that are unbiased while at the same time providing minority representation in compliance with the Voting Rights Act of 1965. The need to draw more majority-minority districts, it is argued, disadvantages the Democrats because it forces the inefficient concentration of overwhelmingly Democratic minority voters.

There are four states with four or more majority-minority districts – California, Texas, Florida, and New York – and they account for more than 60% of the total number of majority-minority districts. Of these, Texas and Florida have statistically significant partisan bias, but California, Illinois, and New York do not, so the need to draw majority-minority districts does not make it impossible to draw unbiased districting plans. Yet many of the states that saw partisan bias increase do have majority-minority districts – or rather a single majority-minority district in most cases. It is possible that packing more minority voters into existing majority-minority districts creates partisan bias.

To test this possibility, we subtract the average percentage of African-Americans and Latinos in districts where those races made up a majority of the population in the 110th Congressional districts from the 113th Congress averages. Figures 3 and 4 display the results for these states. For majority-Latino districts, we find no evidence that states with increased Latino density have more biased redistricting plans.

Figure 3: Majority-Latino District Density Change and Symmetry Change
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Figure 4: Majority-Black District Density Change and Symmetry Change
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By contrast, states with increased majority-Black densities have clearly adopted more biased districting plans. Among the states with substantial reductions in partisan symmetry, only Louisiana (−1.9 %), Ohio (−1.0 %), and Pennsylvania (−0.9 %) had lower average percentages of African Americans in their majority-minority districts after redistricting. The three states with the largest increases in majority-Black district density, Tennessee (5.2 %), North Carolina (2.4 %), and Virginia (2.2 %), include some of the most biased plans in the country. This is not in any way required by the Voting Rights Act – indeed, it reduces the influence of African-American voters by using their votes inefficiently. However, it is consistent with a policy of state legislatures seeking partisan advantage by packing African-American voters, who overwhelmingly vote for the Democratic Party, into districts where the Democratic margin will be far higher than necessary.

Demography is not destiny

The bias we observe is not the inevitable effect of factors such as the urban concentration of Democratic voters or the need to draw majority-minority districts. It is for the most part possible to draw unbiased districting plans in spite of these constraints. Thus if state districting authorities draw districts that give a strong advantage to one party, this is a choice they have made – it was not forced on them by geography. The high level of partisan bias protecting GOP House control can only be explained in political terms. As we show in our book, Pro-Republican bias increased almost exclusively in states where the GOP controlled the districting process.

One of the immediate consequences of unrestrained partisan gerrymandering is that, short of a landslide Democratic victory resembling 2008, the Republicans are very likely to retain control of the House. But one of the more profound consequences is that redistricting has upended one of the bedrock constitutional principles, popular sovereignty. Without an intervention by the courts, political parties are free to manipulate House elections to their advantage without consequence.

 

Economix: Expand the US House

It is good to see the undersized nature of the US House of Representatives get attention in the New York Times‘s Economix blog. The author is Bruce Bartlett, who “held senior policy roles in the Reagan and George H.W. Bush administrations and served on the staffs of Representatives Jack Kemp and Ron Paul”.

Bartlett notes that,

according to the Inter-Parliamentary Union, the House of Representatives is on the very high side of population per representative at 729,000. The population per member in the lower house of other major countries is considerably smaller: Britain and Italy, 97,000; Canada and France, 114,000; Germany, 135,000; Australia, 147,000; and Japan, 265,000.

The strongest empirical relationship of which I am aware between population size and assembly size is the cube root law. Backed by a theoretical model, it was originally proposed by Rein Taagepera in the 1970s. A nation’s assembly tends to be about the cube root of its population, as shown in this graph.*

Fig 7.1

Note the flat line for the USA, indicating lack of increase in House size, since the population was less than a third what it is today. This recent static period is in contrast to earlier times, depicted by the zig-zag black line, in which the USA regularly adjusted House size, keeping it reasonably close to the cube-root expectation.

At only about two thirds of the cube-root value of the population (as of 2010 census), the current US House is indeed one of the world’s most undersized. However, there are some even more deviant cases. Taking actual size over expected size (from cube root) , the USA has the seventh most undersized first or sole chamber among thirty-one democracies in my comparison set. The seven are:

    .466 Colombia
    .469 Chile
    .518 India
    .538 Australia
    .590 Netherlands
    .614 Israel
    .659 USA

As expected, the mean ratio for the thirty-one countries is very close to one (0.992, with a standard deviation of .37). The five most oversized, all greater than 1.4, are France, Germany, UK (at 1.67), Sweden, and Hungary. (The latter was at a whopping 1.80, but has since sharply reduced its assembly size.) Spain, Denmark, Switzerland, Portugal, and Mexico all get the cube root prize for having assembly sizes from .975 to 1.03 of the expectation.

One thing I did not know is that an amendment to the original US constitution was proposed by Madison. According to Bartlett, it read:

After the first enumeration required by the first article of the Constitution, there shall be one representative for every 30,000, until the number shall amount to 100, after which the proportion shall be so regulated by Congress, that there shall be not less than 100 representatives, nor less than one representative for every 40,000 persons, until the number of representatives shall amount to 200; after which the proportion shall be so regulated by Congress, that there shall not be less than 200 representatives, nor more than one representative for every 50,000 persons.

Obviously, Madison’s formula would have run into some excessive size issues over time. And Bartlett does not suggest how much the House should be increased, only noting that its ratio of one Representative for very 729,000 people is excessive. On the other hand, Madison’s ratio of one per 50,000 would produce an absurdly large House! It is just the need to balance the citizen-representative ratio with the need for representatives to be able to communicate effectively with one another that Taagepera devised the model of the cube root, which as we have seen, fits actual legislatures very well.

The cube root rule says the USA “should have” a House of around 660 members today, which would remain a workable size. (If the USA and UK swapped houses, each would be at just about the “right” size!) Even an increase to just 530 would put it within about 80% of the cube root.

As Bartlett notes, at some point the US House will be in violation of the principle of one person, one vote (due to the mandatory representative for each state, no matter how small). However, a case filed in 2009 went nowhere.



* Each country is plotted according to its population, P (in millions), and the size, S, of its assembly. In addition, the size of the US House is plotted against US population at each decennial census from 1830 to 2010.
The solid diagonal line corresponds to the “cube root rule”: S=P^(1/3).
The dashed lines correspond to the cube root of twice or half the actual population, i.e. S=(2P)^(1/3) and S=(.5P)^(1/3).

A variant of the graph will be included in Steven L. Taylor, Matthew S. Shugart, Arend Lijphart, and Bernard Grofman, A Different Democracy (Yale University Press).

An even earlier version of the graph was posted here at F&V in 2005.

Citations are always nice–Increasing the size of the US House

David Fredosso, writing at Conservative Intelligence Briefing, makes the case for increasing the size of the US House, citing one of my previous posts advocating the same. He makes two additional and valuable points: (1) “The Wyoming Rule”, by which the standard Representative-to-population ratio would be that of the smallest entitled unit, is misleading as to how representation is currently (mal-)apportioned; (2) Increasing the size of the House would not, as is sometimes assumed, be of benefit to Democrats and liberals.

David quibbles with the Wyoming part of the story, noting that “Wyoming is not the most overrepresented state — by a long way, that distinction goes to Rhode Island, with its two districts, average population 528,000”, whereas Wyoming has a population of 568,000 (and one seat).

I would note that this is a very small quibble indeed, as the Wyoming Rule–which, to be fair, I neither named nor invented–refers to “smallest entitled unit” not to “most over-represented unit”. Of course, every state is a unit entitled to at least one, but sometimes a state with two members indeed will be over-represented to a greater degree than some state with one member. Whichever we base it on–smallest entitled or most over-represented–the principle is the same: expand the House.

David proposes a House of 535, and has a table of how that would change each state’s current representation. I would go higher (600 or so), but the precise degree of increase is an even smaller quibble. I am pleased to see this idea being promoted in conservative (or liberal, or whatever) circles. And it’s always nice to be cited.

________
See also:

Reapportionment–a better way?; this includes a discussion of the cube-root rule of assembly size, and a graph of how the US relationship of House size to population compares to that of several other countries, and how it has changed over time as the US population has grown, but the House stopped doing so.

US House size, continued

Distortions of the US House: It’s not how the districts are drawn, but that there are (single-seat) districts

In the New York Times, Sam Wang has an essay under the headline, “The Great Gerrymander of 2012“. In it, he outlines the results of a method aimed at estimating the partisan seat allocation of the US House if there were no gerrymandering.

His method proceeds “by randomly picking combinations of districts from around the United States that add up to the same statewide vote total” to simulate an “unbiased” allocation. He concludes:

Democrats would have had to win the popular vote by 7 percentage points to take control of the House the way that districts are now (assuming that votes shifted by a similar percentage across all districts). That’s an 8-point increase over what they would have had to do in 2010, and a margin that happens in only about one-third of Congressional elections.

Then, rather buried within the middle of the piece is this note about 2012:

if we replace the eight partisan gerrymanders with the mock delegations from my simulations, this would lead to a seat count of 215 Democrats, 220 Republicans, give or take a few.

In other words, even without gerrymandering, the House would have experienced a plurality reversal, just a less severe one. The actual seat breakdown is currently 201D, 234R. In other words, by Wang’s calculations, gerrymandering cost the Democrats seats equivalent to about 3.2% of the House. Yes, that is a lot, but it is just short of the 3.9% that is the full difference between the party’s actual 201 and the barest of majorities (218). But, actually, the core problem derives from the electoral system itself. Or, more precisely, an electoral system designed to represent geography having to allocate a balance of power among organizations that transcend geography–national political parties.

Normally, with 435 seats and the 49.2%-48.0% breakdown of votes that we had in 2012, we should expect the largest party to have about 230 seats. ((Based on the seat-vote equation.)) Instead it won 201. That deficit between expectation and reality is equivalent to 6.7% of the House, suggesting that gerrymandering cost the Democrats just over half the seats that a “normally functioning” plurality system would have netted it.

However, the “norm” here refers to two (or more) national parties without too much geographic bias to where those parties’ voters reside. Only if the geographic distribution is relatively unbiased does the plurality system work for its supposed advantage in partisan systems: giving the largest party a clear edge in political power (here, the majority of the House). Add in a little bit of one big party being over-concentated, and you can get situations in which the largest party in votes is under-represented, and sometimes not even the largest party in seats.

As I have noted before, plurality reversals are inherent to the single-seat district, plurality, electoral system, and derive from inefficient geographic vote distributions of the plurality party, among other non-gerrymandering (as well as non-malaportionment) factors. Moreover, they seem to have happened more frequently in the USA than we should expect. While gerrymandering may be part of the reason for bias in US House outcomes, reversals such as occurred in 2012 can happen even with “fair” districting. Wang’s simulations show as much.

The underlying problem is, again, because all the system really does is represent geography: which party’s candidate gets the most votes here, there, and in each district? And herein lies the big transformation in the US electoral and party systems over recent decades, compared to the party system that was in place in the “classic” post-war system: it is no longer as much about local representation as it once was, and is much more about national parties with distinct and polarized positions on issues.

Looking at the relationship between districts and partisanship, John Sides, in the Washington Post’s Wonk Blog, says “Gerrymandering is not what’s wrong with American politics.” Sides turns the focus directly on partisan polarization, showing that almost without regard to district partisanship, members of one party tend to vote alike in recent congresses. The result is that when a district (or, in the Senate, a state) swings from one party to another, the voting of the district’s membership jumps clear past the median voter from one relatively polarized position to the other.

Of course, this is precisely the point Henry Droop made in 1869, and that I am fond of quoting:

As every representative is elected to represent one of these two parties, the nation, as represented in the assembly, appears to consist only of these two parties, each bent on carrying out its own programme. But, in fact, a large proportion of the electors who vote for the candidates of the one party or the other really care much more about the country being honestly and wisely governed than about the particular points at issue between the two parties; and if this moderate non-partisan section of the electors had their separate representatives in the assembly, they would be able to mediate between the opposing parties and prevent the one party from pushing their advantage too far, and the other from prolonging a factious opposition. With majority voting they can only intervene at general elections, and even then cannot punish one party for excessive partisanship, without giving a lease of uncontrolled power to their rivals.

Both the essays by Wang and by Sides, taken together, show ways in which the single-seat district, plurality, electoral system simply does not work for the USA anymore. It is one thing if we really are representing district interests, as the electoral system is designed to do. But the more partisan a political process is, the more the functioning of democracy would be improved by an electoral system that represents how people actually divide in their partisan preferences. The system does not do that. It does even less well the more one of the major parties finds its votes concentrated in some districts (e.g. Democrats in urban areas). Gerrymandering makes the problem worse still, but the problem is deeper: the uneasy combination of a geography-based electoral system and increasingly distinct national party identities.

Spurious majorities in the US House in Comparative Perspective

In the week since the US elections, several sources have suggested that there was a spurious majority in the House, with the Democratic Party winning a majority–or more likely, a plurality–of the votes, despite the Republican Party having held its majority of the seats.

It is not the first time there has been a spurious majority in the US House, but it is quite likely that this one is getting more attention ((For instance, Think Progress.)) than those in the past, presumably because of the greater salience now of national partisan identities.

Ballot Access News lists three other cases over the past 100 years: 1914, 1942, and 1952. Sources disagree, but there may have been one other between 1952 and 2012. Data I compiled some years ago showed a spurious majority in 1996, if we go by The Clerk of the House. However, if we go by the Federal Election Commission, we had one in 2000, but not in 1996. And I understand that Vital Statistics on Congress shows no such event in either 1996 or 2000. A post at The Monkey Cage cites political scientist Matthew Green as including 1996 (but not 2000) among the cases.

Normally, in democracies, we more or less know how many votes each party gets. In fact, it’s all over the news media on election night and thereafter. But the USA is different. “Exceptional,” some say. In any case, I am going to go with the figure of five spurious majorities in the past century: 1914, 1942, 1952, 2012, plus 1996 (and we will assume 2000 was not one).

How does the rate of five (or, if you like, four) spurious majorities in 50 elections compare with the wider world of plurality elections? I certainly do not claim to have the universe of plurality elections at my fingertips. However, I did collect a dataset of 210 plurality elections–not including the USA–for a book chapter some years ago, ((Matthew Soberg Shugart, “Inherent and Contingent Factors in Reform Initiation in Plurality Systems,” in To Keep or Change First Past the Post, ed. By André Blais. Oxford: Oxford University Press, 2008.)) so we have a good basis of comparison.

Out of 210 elections, there are 10 cases of the second party in votes winning a majority of seats. There are another 9 cases of reversals of the leading parties, but where no one won over 50% of seats. So reversals leading to spurious majority are 4.8% of all these elections; including minority situations reversals are 9%. The US rate would be 10%, apparently.

But in theory, a reversal should be much less common with only two parties of any significance. Sure enough: the mean effective number (N) of seat-winning parties in the spurious majorities in my data is just under 2.5, with only one under 2.2 (Belize, 1993, N=2.003, in case you were wondering). So the incidence in the US is indeed high–given that N by seats has never been higher than 2.08 in US elections since 1914, ((The original version of this statement, that “N is almost never more than 2.2 here” rather exaggerated House fragmentation!)) and that even without this N restriction, the rate of spurious majorities in the US is still higher than in my dataset overall.

I might also note that a spurious majority should be rare with large assembly size (S). While the US assembly is small for the country’s population–well below what the cube-root rule would suggest–it is still large in absolute sense. Indeed, no spurious majority in my dataset of national and subnational elections from parliamentary systems has happened with S>125!

So, put in comparative context, the US House exhibits an unusually high rate of spurious majorities! Yes, evidently the USA is exceptional. ((Spurious majorities are even more common in the Senate, where no Republican seat majority since at least 1952 has been based on a plurality of votes cast. But that is another story.))

As to why this would happen, some of the popular commentary is focusing on gerrymandering (the politically biased delimitation of districts). This is quite likely part of the story, particularly in some sates. ((For instance, see the map of Pennsylvania at the Think Progress link in the first footnote.))

However, one does not need gerrymandering to get a spurious majority. As political scientists Jowei Chen and Jonathan Rodden have pointed out (PDF), there can be an “unintentional gerrymander,” too, which results when one party has its votes less optimally distributed than the other. The plurality system, in single-seat districts, does not tote up party votes and then allocate seats in the aggregate. It only matters in how many of those districts you had the lead–of at least one vote. Thus a party that runs up big margins in some of its districts will tend to augment its total in its “votes” column at a faster rate than it augments its total in the “seats” column. This is quite likely the problem Democrats face, which would have contributed to its losing the seat majority despite its (apparent) plurality of the votes.

Consider the following graph, which shows the distribution (via kernel densities) of vote percentages for the winning candidates of each major party in 2008 and 2010.

Kernel density winning votes 2008-10
Click image for larger version

We see that in the 2008 concurrent election, the Democrats (solid blue curve) have a very long and higher tail of the distribution in the 70%-100% range. In other words, compared to Republicans the same year, they had more districts in which they “wasted” votes by accumulating many more in the district than needed to win it. Republicans, by contrast, tended that year to win more of their races by relatively tighter margins–though their peak is still around 60%, not 50%. I want to stress, the point here is not to suggest that 2008 saw a spurious majority. It did not. Rather, the point is that even in a year when Democrats won both the vote plurality and seat majority, they had a less-than optimal distribution, in the sense of being more likely to win by big margins than were Republicans.

Now, compare the 2010 midterm election, in which Republicans won a majority of seats (and at least a plurality of votes). Note how the Republican (dashed red) distribution becomes relatively bimodal. Their main peak shifts right (in more ways than one!) as they accumulate more votes in already safe seats, but they develop a secondary peak right around 50%, allowing them to pick up many seats narrowly. That the peak for winning Democrats’ votes moved so much closer to 50% suggests how much worse the “shellacking” could have been! Yet even in the 2010 election, the tail on the safe-seats side of the distribution still shows more Democratic votes wasted in ultra-safe seats than is the case for Republicans. ((It is interesting to note that 2010 was very rare in not having any districts uncontested by either major party.))

I look forward to producing a similar graph for the 2012 winners’ distribution, but will await more complete results. A lot of ballots remain to be counted and certified. The completed count is not likely to reverse the Democrats’ plurality of the vote, however.

Given higher Democratic turnout in the concurrent election of 2012 than in the 2010 midterm election, it is likely that the distributions will look more like 2008 than like 2010, except with the Republicans retaining enough of those relatively close wins to have held on to their seat majority.

Finally, a pet peeve, and a plea to my fellow political scientists: Let’s not pretend there are only two parties in America. Since 1990, it has become uncommon, actually, for one party to win more than half the House votes. Yet my colleagues who study US elections and Congress continue to speak of “majority”, by which they mean more than half the mythical “two-party vote”. In fact, in 1992 and every election from 1996 through at least 2004, neither major party won 50% of the House votes. I have not ever aggregated the 2006 vote. In 2008, Democrats won 54.2% of the House vote, Republicans 43.1%, and “others” 2.7%. I am not sure about 2010 or 2012. It is striking, however, that the last election of the Democratic House majority and all the 1995-2007 period of Republican majorities, except for the first election in that sequence (1994), saw third-party or independent votes high enough that neither party was winning half the votes.

Assuming spurious majorities are not a “good” thing, what could we do about it? Democrats, if they are developing a systematic tendency to be victims of the “unintentional gerrymander”, would have an objective interest in some sort of proportional representation system–perhaps even as much as that unrepresented “other” vote would have.