Gerrymandering: Finding the Deviant Elections

During oral argument in Rucho v. Common Cause, the North Carolina gerrymandering case, the Supreme Court and the attorneys for the parties considered a variety of criteria to identify what Justice Stephen Breyer called “real outliers” in terms of election results. In the first article of this series I considered his half-the-vote/one-third-the seats criterion. In the last posting I considered the notion of measuring deviations from some predicted baseline result. In that article I proposed a formula for estimating the baseline based on historical voting data:

Expected % Democratic Seats = 2 X (% Democratic Two-Party Votes) – 50

This formula provides a simple, yet historically accurate baseline for estimating the share of seats we should expect the Democrats to win given their share of the Congressional vote statewide. (I should note that this formula is entirely symmetric. We could use the Republican vote and seat shares and get the identical result.) Armed with a method for determining the baseline prediction, I turn now to a method for identifying deviant electoral results.

Measuring the Deviation

How big a deviation from that baseline should be considered “significant” depends on both statistical and legal/constitutional criteria. I will only be talking about “significance” in the statistical sense. As we’ll see, the size of the deviation you are willing to tolerate depends on the proportion of outcomes you consider to be possibly unconstitutional.  In that sense, Justice Potter Stewart’s famous comment about identifying pornography, “I know it when I see it,” applies to gerrymandering just as well.

In the discussion about proportionality, plaintiff’s attorney Paul Stewart suggested and dismissed a “one standard deviation” away from some baseline criterion for gerrymandering. I have dealt with his objection concerning estimating a baseline result, but just one standard deviation is much too low a bar. As this graph shows, about 32% of elections should fall outside the one-standard-deviation criterion, many too many to qualify for judicial review. Statisticians often use two standard deviations as a minimal criterion for “statistical significance.” That would subject about five percent of the elections to additional scrutiny. Justice Breyer’s criterion works out to about one election in a thousand, which corresponds to a standard deviation difference of about 2.5.

Now it turns out the regression method also generates an estimate of the “standard deviation” of the predicted values. This quantity is called the “standard error,” and for the regression using state-years as the unit of analysis, the estimated standard error for the percent of seats won is 10.2.  So, using two standard errors as a minimum criterion, we should look for results where the difference between the actual number of seats won, and the prediction from the formula above, is at least 20 percent.  Here are the elections held since 2010 where the actual outcome differs from the predicted value by a least 20 percent. The “standardized deviation” column measures the absolute value of the quantity (Actual – Predicted)/(Standard Error).  The larger the value the further the election deviated from the prediction. Using the absolute value treats both parties symmetrically.

All three elections identified by the “Breyer criterion” also appear in this list. However there are a number of elections that fail his criterion, but where the actual seat outcome differs from the predicted value by at least two standard errors.  Connecticut persistently sent five Democrats to Congress since 2010 when the vote suggests there should have been at least one Republican in the delegation. Connecticut would not be identified by Breyer’s criterion, but a reasonable observer would conclude that state’s Congressional district lines appear to have been gerrymandered in the Democrats’ favor. Democrats also got “too many” seats in Maryland in 2014, but that pattern did not recur in other elections since the 2010 Census. Similar “one-offs” like VA12, NJ18, and MI12 might also be attributed to chance rather than systematic discrimination via gerrymandering.

Most of the other elections in the list show an excess number of Republicans winning House seats given the statewide vote for Democrats. Both North Carolina and Pennsylvania appear twice as does Ohio, whose map was just thrown out by a Federal court.

By either Breyer’s criterion or by measuring deviations from a predicted baseline, the map created by the North Carolina legislature qualifies as gerrymandered. Ohio and Connecticut also deserve judicial scrutiny.

Technical Appendix for Gerrymandering and Proportionality

These regressions measure the relationship between the percent of seats awarded to Democrats as a function of the percent of votes that party won. The “national-level” figures represent a regression using election-years as the unit of analysis; data spans 1940 through 2018 or forty observations. The “state-level” estimates come from regression using state-years as the unit of analysis. There are 679 qualifying races.  See this article for details on how states and elections were selected. State-years where one-party won all the seats are excluded.

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Gerrymandering and “Proportionality:” Setting the Baseline

In my last post I considered what I called the “Breyer criterion” for identifying partisan gerrymandering — a party winning half the vote in a state receives only a third of the seats.  That criterion identified just seven races out of the nearly eight hundred I examined, or just 0.9 percent of the state-level elections to Congress where candidates of both major parties stood. Breyer proposed his criterion to identify “real outliers,” elections that are “really extraordinary.” A one-in-a-thousand criterion probably fits that definition.

However the Court also discussed the general concept of how to measure “proportionality” between seats and votes. The attorney for the plaintiffs, Paul Clement, brought up the notion of a “one standard deviation from proportional representation” criterion mostly as a straw horse. Leaving aside his use of “proportional representation,” which as the oral argument shows is fraught with constitutional issues, Clement then claimed that it is impossible to know what the correct baseline should be from which to measure seat outcomes.

So I think the fundamental problem is there is no one standard deviation from proportional representation clause in the Constitution. And, indeed, you can’t talk even generally about outliers or extremity unless you know what it is you’re deviating from.

Clement’s argument ignores decades of political science research into the relationship between votes won and seats awarded.  Studies dating back to at least 1948 have theorized about and examined empirically the relationship between seats and votes.

Measuring the Baseline

I’ve written a number of times about the relationship between votes won and seats awarded in “first-past-the-post” or “plurality” electoral systems like ours.  These types of electoral systems routinely award the majority winner of the vote a disproportionately greater share of seats. Here is a simple example, using national electoral results for Congress.

The dark blue line represents the “best-fit” relationship between the percent of votes won by the Democrats in each election year and the percent of House seats the party won using simple “ordinary least squares” regression. The historical relationship is substantially steeper than the thin line in the chart representing parity, or when a party’s share of seats equals its share of votes.1

Using simple regression the equation that best describes this relationship is, in round numbers,2

% Seats Democrat = 2 X (% Votes Democrat) – 50

So, for instance, in a year when the Democrats win 55 percent of the vote, they should receive on average (2 X 55) – 50 = 60 percent of the seats.

Since gerrymanders take place at the state level, data from national elections do not provide the correct basis for determining whether a particular state’s election deviated “too far” from some predicted baseline. To develop such a baseline for Congressional elections I turn again to the MIT database of Congressional races I used in the preceding blog post.  Here is the relationship between votes and seats for state-year combinations. Each point represents a general election in a given state in a particular year, like Alabama in 1976.

A number of races resulted in one party or the other winning all the seats. These unanimous outcomes pose mathematical problems for our method, so I excluded those 84 races in the calculation of the slope and intercept for the regression line in the chart.

(The horizontal lines come from states with small numbers of districts where the number of outcomes is mathematically restricted. For instance, a state with four districts will often return a 3-1 result for one party. That leads to clustering at values of 25 or 75 percent.)

Using state-level election results gives us a model that is numerically quite similar to the simple method based on election years above:

% Seats Democrat = 2.3 X (% Votes Democrat) – 66

Here the slope of the line is slightly steeper than two and the intercept slightly more negative. In practice, though, the difference between these results and predictions using the simpler model from national-level data are negligible. The lines are so close that I could not represent them both on the chart.

Given the convergence between these two sets of estimates, I propose that

The best “baseline” estimate for the division of seats given the division of the vote in state-level Congressional elections is

% Seats Democrat = 2 X (% Votes Democrat) – 50

That formula uses simple numbers like two and fifty and produces results nearly identical to those using the estimated regression coefficients of 2.3 and -66.

The regression method also produces a measure of the “standard deviation” of actual outcomes around the predicted values. I use that quantity in the next post to identify potential gerrymanders using the deviation from proportionality method.

1The results for the last two Democratic off-year House victories, retaking the chamber in 2006 and 2018, both fall on this parity line. Given the historical relationship, the Democrats did not receive the usual reward in the House for their victories in the popular vote. The elections in 2012 and 2018 also show significant negative effects for Democrats.

Gerrymandering and the “Breyer Criterion”

On March 26th the Supreme Court heard oral argument in Rucho v. Common Cause. The case concerns whether North Carolina’s post-2010 electoral map so disadvantages Democratic candidates that it should be ruled unconstitutional. This case raises many Constitutional and legal issues that fall outside the purview of this blog; for instance, whether the Republican-controlled North Carolina legislature showed the intent to discriminate against Democrats in their choice of map. However some of the issues raised during oral argument lend themselves to empirical examination.

A persistent concern during oral argument was whether “proportionality” should be used as a Constitutional standard to determine if a particular electoral outcome might be ruled unconstitutional.  In one of these discussions Justice Stephen Breyer proposed that “when a party wins a majority of the votes in a state, … but the other party gets more than two-thirds of the seats” the result could be declared unconstitutional.

How frequently might Justice Breyer’s criterion apply to actual state-level results comparing votes cast for Congress and the proportion of seats awarded? The Court has an incentive to establish a highly-restrictive criterion to deter future filings by state parties hoping to overturn an unfortunate result. How restrictive is the Breyer criterion? How often might we see electoral results flagged as potentially unconstitutional by the workings of this rule?

What Elections to Analyze

To address these questions, I begin with an invaluable dataset compiled by the MIT Election Lab. It comprises election returns for all candidates who ran for Congress between 1976 and 2018. Using these candidate records as a basis, I created a new aggregated dataset containing results by party for each combination of state and election year.

In the process I eliminated a number of records from consideration. First, because it is impossible to gerrymander a state with just one Congressional district, I excluded any state-year combinations when the state was apportioned into a single district. Examples include Alaska and Wyoming throughout the 1976-2018 period, and states like Montana and Nevada in the years when they had but one district.

I further eliminated states with just two Congressional districts. In those cases an election would fit the criterion if one party won over half the vote and lost both seats. However that outcome would occur by random chance a quarter of the time if both seats had even odds of going to either party.  Courts would likely not be willing to rule a particular seat distribution was unconstitutional when the result could have happened by chance a quarter of the time. As a result I also removed state-years when the state was apportioned only two seats.

Even this set of races needs further refinement to use as a basis to examine Breyer’s criterion. The canonical notion of a two-party race between a Democrat and a Republican dissolves once we look at the data.  Most races include minor candidates and not every seat has both a Democratic and a Republican contender.  Many seats were left uncontested over this period by one or the other major party, especially in the South.  And with the introduction of “top-two” voting in California and Washington, general elections can pit two Democrats or two Republicans against one another.

So I further limited the sample by selecting only Congressional elections with both a Democratic and a Republican contender. That left a total of 7,701 eligible races which I then aggregated to the level of state-years, e.g., Alabama in 1976. Some state-year combinations then had fewer than three contested races; those observations were also excluded. That left me with a total of 799 state-years for the analysis to follow.

Justice Breyer’s Criterion

So in this sample of nearly eight hundred Congressional outcomes, how often do we find the particularly egregious combination where a party won at least half the Congressional vote in a state but was awarded fewer than a third of the seats.

In practice Breyer’s criterion turns out to be highly restrictive.  Of the 799 Congressional elections that qualified for my sample, only seven (0.9 percent) would have fit his rule.  Moreover, only four seats were contested in the three Alabama races and the one in South Carolina. Assuming even odds of each seat electing a Democrat, but a Democratic majority overall, the chance of getting an outcome with at least three Republican seats is 1/8.1 Intuitively that seems too low a bar for declaring a particular result unconstitutional.

Of more interest is that three of the seven Alabama seats, and two seats in the South Carolina race, were uncontested. The totals for these states represent the votes cast and seats awarded in the contested districts. Leaving seats uncontested may itself be an indicator of gerrymandering, If maps are too distorted, it may make little sense for a party to invest resources in races where their opponents are certain to be victorious.

Pennsylvania and North Carolina are another story entirely though.

Breyer’s criterion flags three elections in those states. all of which took place after the 2010 Census. Since then both states have become poster children for gerrymandering. The Pennsylvania map that took effect in 2012 awarded Republicans fully thirteen of the state’s eighteen seats while the Democrats won the popular vote statewide by a small margin. The Pennsylvania State Supreme Court ruled in January, 2018, that the Congressional map was so unfair that it violated the state’s own Constitution. The Court threw out the map and later that month commissioned Stanford Law School professor Nate Persily to draw a new one.  The 2018 election using the redrawn district lines resulted in a 9-9 tie, compared to the 13-5 advantage Republicans had maintained since 2010.

North Carolina is, of course, the state at issue in Rucho v Common Cause, so it is appropriate that it should be flagged here as well. Twice since the 2010 Census have the Democrats won a small majority of the popular vote, but were awarded only three or four of the state’s thirteen Congressional seats. So if Justice Breyer wanted to establish a criterion that would pick out the most egregious partisan gerrymanders, his one-half the vote/one-third the seats rule seems to fit the requirement.

Justice Breyer’s rule was not the only criterion discussed in oral arguments that day. Both plaintiff’s attorney Paul Clement and Justice Neal Gorsuch discussed a measure based on the difference between a state’s actual seat distribution and some measure of what its “proportionate” share might be. I turn to that subject in my next posting.

1Imagine a state with four districts. In three of them the Democrats and Republicans tie. In the fourth seat the Democrats win by one. That gives them a one-vote majority in the popular vote and one seat. If we flip a coin for each of the three tied districts, a result with three Republicans occurs one time in eight. I  thank my friend Jim Stodder for making me rethink the calculation of this probablity.

No, the “Blue Wave” did not wash away gerrymandering

Democrats have won, on average, about eight fewer seats in each election since 2010 than we would expect given their popular vote.  The surge in Democratic votes this year might have cut that deficit down to two, but it is more likely there was no effect at all.

Before the November election, some commentators argued that a surge in turnout could negate the effects of Republican gerrymandering after 2010.  Of course, this argument only makes sense if there were a larger increase in Democratic turnout than Republican turnout.  A proportional increase for both parties would leave the seat results unchanged.

It is certainly true that the Democratic vote for the House of Representatives was considerably greater in 2018 than it was in 2014.  In fact, Democrats cast nearly as many votes this month as they did for Hillary Clinton two years ago.  Compared to the 2014 midterm, the Democrats increased their vote by over fifty percent. Republicans also turned out in higher numbers, recording a vote for House candidates some 23 percent above their 2014 totals. (Figures for 2018 from Dave Wasserman of Cook Political Report.)

Was this surge in Democratic turnout sufficient to overcome the 2010 gerrymander?

To test this, I added a term for the 2018 election to my standard model of seats and votes described here and here.  I use the “logits” of Democratic seats and votes won with “dummy variables” to represent reapportionment periods.  The basic model, with 2018 included, produces this chart showing the number of Democratic seats won or lost compared to what we would expect based on the national popular vote won by that party.  Some periods, like 2002-2010, show no significant excess gains or losses.  Others like 1942-1950 and 2012-2018 show substantial effects.In the five elections beginning in 1942, Democrats routinely won nearly nine more House seats than their popular vote would predict.  Republicans picked up a number of state legislatures in the 1952 election and erased this deficit for the decade to follow.  From 1962 through 1990, Democrats were again advantaged, but by a diminishing margin over time.  The elections fought between 1992 and 2010 showed no systematic bias for either party  After the 2010 Census and the “shellacking” of Democrats in both national and state elections that year, Republicans were able to draw district maps that gave their party just short of eight “excess” seats in the House.

By adding another variable to represent just the 2018 election, it does indicate a diminished effect compared to the 2012-2018 average.  However this effect fails to reach any conventional level of statistical significance (t = 1.07).

One other question we might ask is what the 2018 outcome would have been had the neutral results for 1992-2010 continued on into elections held since the 2010 Census.  While the chart above shows that Democrats lost on average about eight seats to gerrymandering beginning in 2012, the estimated effect for this past election is just short of fourteen seats, the result of the Democrats’ substantial victory in the popular vote.

Governors and Gerrymandering: Update

Democratic governors in seven “red” states, and Republicans in two “blue” ones, will help insulate 81 likely Congressional seats from gerrymandering after 2020. Redistricting for another 61 seats will likely remain entirely in Republican hands compared to just seven seats in states with unified Democratic control.

Yesterday’s election helped limit potential gerrymandering after the 2020 Census in a half-dozen states but not, unfortunately, in the largest prizes.  Democrats appear to have failed in their bids to win the gubernatorial elections in Florida, Georgia, and Ohio, and in all three states Republicans maintained their control over the state legislatures as well.  Barring Democratic legislative victories, all three of those states will remain prospects for Republican gerrymanders in 2021.

Democrats did win or retain the governorships in Colorado, Connecticut, Illinois, Maine, Minnesota, Pennsylvania, and Wisconsin and will likely face either Republican or split legislatures when redistricting maps are redrawn after 2020.  Together those states will probably encompass 64 Congressional districts after reapportionment.  Two states, Maryland and Massachusetts, with a likely total of seventeen seats, will see Republican governors facing off against Democratic legislatures in 2021.  I would not be surprised to see a new Republican representative sent to Washington after the 2020 Census from both these states which now have uniformly Democratic Congressional delegations.

Because the Democrats failed to win the governors’ races in Florida, Georgia, and Ohio, all three states will be prime targets for Republican gerrymanders in 2021.  (Iowa, with its four Members of Congress, matters much less.)  Ohio and Florida accounted for three to five “excess” Republican seats after the 2010 Census, and Georgia may have added another.  Because the Democrats fared less well in these larger states, the GOP will be drawing district lines for 61 of the 149 seats in “trifecta” states where they control both the governor’s mansion and the two houses of the state legislature.

1Both Michigan and New York appeared in the earlier version of this chart.  However both states will be using nonpartisan redistricting commissions in 2021 and have been excluded from the analysis here.

Governors and Gerrymanders in 2021

Elections this fall may limit the extent of gerrymandering for some 200 House seats after the 2020 Census.

Americans will elect thirty-four governors to four-year terms this fall, giving them all a say in how their states’ Congressional and legislative districts will be drawn after the 2020 Census.1

In 2010, Republicans took control of many state legislatures and governors’ offices, which offered them the opportunity to draw district maps that favored their party. During 2011-2012 when those maps were drawn, Republicans controlled both the executive and legislative branches in nineteen states and appear to have won fourteen percent more House elections in those states than we might expect based on historical data.  Democrats controlled just eight states and won four percent more seats than expected.  In thirteen states partisan control was split between the branches, and there the partisanship of the governor appears to have been the controlling factor. In split control settings, the governor’s party won about six percent more House seats after 2010 than expected.

The election in November has the potential for influencing how dozens of Congressional district lines will be drawn in the aftermath of the 2020 Census.  In a number of states Democrats are poised to break the Republicans’ lock on control of government by taking back the governor’s mansion.

I have categorized the governors’ races by their competitiveness using the most recent ratings for those races as compiled at Wikipedia.  Since the next redistricting will involve the results of the 2020 Census, I have used state-level population projections to estimate the number of seats each state will be awarded after reapportionment.  Most states’ representation in Congress will not change, but a few states like Texas are projected to add seats, while Rhode Island may lose one of its two representatives in the House.  Forecasting the results of state legislative races this fall, and more importantly two years hence, is obviously a dicey proposition.  I have instead assumed that all legislatures will be controlled by the same parties that control them now.  Based on these data I estimate that redistricting for some 188 seats, or 43 percent of the House, may be affected by the results of this year’s gubernatorial elections.

An “S” (“split”) code in the legislative column indicates that the two houses of the state legislature are held by different parties.

The first two columns of this table present the likely outcome of this fall’s race for governor in each of these states.  The “Consensus Rating” is based on translating each prognosticator’s ratings like “Safe Republican” or “Likely Democrat” into a numerical score and averaging them.  I also present the most recent ratings for each race from the well-known site, FiveThirtyEight.com.

In these more competitive states Democratic candidates for governor appear to be well-positioned to win back these offices from the Republicans.  Only in Massachusetts and Maryland are we likely to see Republican governors winning re-election while their states’ legislatures remain in Democratic hands.  In ten states from Georgia to Michigan to New Mexico, Democratic candidates are poised to oust Republican governors even if their states’ legislatures do not change hands.  As my results from the post-2010 redistricting showed, governors appear to have most of the clout in redistricting battles, reducing the chances of gerrymandering in places like Michigan, Ohio and Florida, all of which had an “excess” number of Republican seats beginning with the 2012 election.

1Governors in New Hampshire and Vermont serve two-year terms.

Governors Hold the Cards in Congressional Redistricting

In “split-control” states, Republicans won 6.2 percent more seats than expected when they held the governorship; when Democrats held that office, Republicans won 6.5 percent fewer seats than expected.

Americans will elect thirty-four governors to four-year terms this fall.  They will still be in office after the 2020 Census and will have a say in how states redraw their Congressional and legislative district plans. All states where legislatures draw district lines except North Carolina grant the governor the power to veto any plan.  In states where control over the branches is split between the parties, this process should lead to compromises acceptable to both parties.  As well see, however, the evidence from the redistricting after the 2010 Census suggests governors hold all the cards.

In nine states, politicians play no direct role as redistricting is left up to nonpartisan commissions.  Courts, too, can override the lines drawn by legislatures.  This year’s dramatic redrawing of the lines in Pennsylvania follows similar judicial interventions in Florida and New York.  The New York decision affects my analysis since it applied to elections beginning with 2012.  (The other decisions have yet to come into force.)  I have added New York to the commission list, but have analyzed it, and California, separately as well.

I have also excluded the seven states which have only one Congressional district like Wyoming and Alaska since gerrymandering is not possible with no lines to draw.  That leaves 43 states which can be categorized as follows:

• maps drawn by nonpartisan commissions or courts (8 states);
• maps drawn by Republican legislatures facing Republican governors (16 states)
• maps drawn by Democratic legislatures facing Democratic governors (6 states); and,
• maps drawn when either the houses of the legislature were held by opposing parties, or where the legislature had unified control but faced a governor of the opposite party (13 states).

To avoid relying too heavily on a single year, I have added together the votes cast for Republican and Democratic House candidates in each group of states for the 2012-2016 elections.  I have applied the same method to seats won, again summing up the number of Republican and Democratic seats won across all three elections.  That method produces these results:

House Votes and Seats Won 2012-2016 by Redistricting Method

The first column reports the Republican percent of the total two-party popular vote summed across the three elections, 2012, 2014, and 2016.  In the sixteen states where Republicans held both houses of the state legislature and the governorship, they won 56.5 percent of the two-party House vote and 71.7 percent of the seats.  In solidly Democratic states the Republicans won both a minority of the popular vote and of the seats awarded.  The results for commissions and courts is complex; I will deal with it in a later article.

In various articles here I have described the natural inflation of the proportion of seats won due to the operation of our first-past-the-post electoral system.  As parties win larger and larger proportions of the vote, they gain an ever-increasing share of seats.  I have estimated this inflation factor using both biennial election results back to 1946, and across states in 2012.  Both methods produce equivalent results, for instance.

To estimate the share of seats awarded you need only square1 the value of the ratio (Republican Votes)/(Democratic Votes) to get the ratio (Predicted Republican Seats)/(Predicted Democratic Seats).  This approach gives rise to the third column in the table, the proportion of seats that are predicted to be won by the Republicans after applying this “square law” rule.2 In the entry for Republican control, that party’s 56 percent share of the House vote should produce a share of about 63 percent of seats.  In practice, the Republicans won nearly 72 percent of the seats.  The final column measures the over- or under-representation of the Republicans in the House as a percentage gain or loss compared to the predicted share.  In this case, the Republican’s 72 percent is about 14 percent higher than the expected 63 percent. This figure provides a criterion for evaluating how over- or under-advantaged a party was compared to expectations.

The normal expectations for states with unified control are confirmed:  Republicans win a disproportionate share of seats in states where they controlled the redistricting process, and won disproportionately fewer seats than expected in states where the Democrats were in control.  Notice that the size of Republican advantage in states that party controlled is larger than the disadvantage the Republicans faced in states controlled by Democrats, +14 percent versus -4 percent.

By this measure states with some form of split party control show hardly any partisan advantage at all.  Republicans won a share of the seats awarded in these states nearly equal to their expected share.  However, it turns out this overall result hides a lot of significant variation.

We can identify two different forms of split control:

• ones where both chambers of the state legislature are held by one party but the governor is of the opposite party; and,
• ones where the chambers of the state legislature are held by different parties.

As it turns out there are nearly equal number of each type of split control; in seven states unified legislatures faced an opposition governor, while in six states the chambers themselves were split.  Once we break out these various patterns, the power of governors becomes clear.  In both types of split control, the governor’s party is disproportionately advantaged during redistricting.  In fact, if we group these split-control states together simply by the partisanship of the governor, Republicans were over-represented in seats awarded by 6.2 percent where they held the governorship; when Democrats held that office, Republicans were under-represented by 6.5 percent.

These results are rather striking.  They suggest that opposite-party governors can force a redistricting map that is actually more favorable to the governor’s party than to the legislature’s.  Similarly when the two legislative chambers are held by opposite parties, it is again the governor who appears to determine which map wins approval.  It appears the governor’s veto is a more powerful weapon in the fight over Congressional district lines than the legislature’s control over drawing the lines themselves.  This fact could weigh heavily over redistricting fights in states like Colorado, Michigan, Florida and Georgia where Democratic governors may win election and end up facing Republican legislatures.  In Massachusetts and Maryland the reverse will likely hold true.

1The longitudinal estimate was 2.04; the cross-sectional estimate was 2.08. For simplicity I have rounded down to two, which is well within the confidence intervals for each estimate of beta.

2The tendency for first-past-the-post systems to disproportionately advantage the winning party was first observed in elections in the United Kingdom. There the coefficient reached three, giving rise to the name “cube law” rule, since cubing the ratio (Labour Votes)/(Conservative Votes) does a good job of predicting the ratio (Labour Seats/Conservative Seats). Following this tradition, I have named the US version of this relationship the “square law” rule.

Can the Democrats Retake the House in 2018?

Now that all the gnashing of teeth has ended after the Republicans managed to hold on to the Georgia Sixth, perhaps we can step back and take a more systematic look at the Democrats’ prospects in 2018. Democrats will likely not make any gains in the Senate since the Republicans have only eight seats at-risk compared to twenty-three Democrats and both independents, Maine’s Angus King and Vermont’s Bernie Sanders.  That leaves the House as the only target.

There are two steps involved in answering this question.  The first is to use our historical experience with House elections to examine how votes are translated into seats.  With that information we can estimate the proportion of the two-party House vote that the Democrats need to win to take back the House in 2018.

As I wrote back in 2012, a combination of geographic clustering by party and good old partisan gerrymandering has created a “Republican bulwark” in the House since the last redistricting after the 2010 Census.  That means that the Democrats will need to win more than a majority of the popular vote for Congress if they intend to win a majority of House seats.

I have refined this simple seats and votes model in two ways.  First, I let the “swing ratio” vary between two historical periods, 1940-1992 and 1994-2016. Empirically the effects of voting “swings” on seat “swings” is significantly smaller in the more recent period.  As Tufte argues in his classic paper on the seats/votes relationship, a decline in the swing ratio indicates an increase in the proportion of “safe” seats.  As fewer and fewer seats have vote shares around fifty percent, there are consequently fewer that can be “flipped” by an equivalent shift in voters’ preferences.

I also use the results for the 2014 and 2016 elections to more sharply estimate the effect since 2010.  If we calculate the popular vote share required for the Democrats to win half the seats in the House, they would need to secure a bit over 53 percent of the (two-party) votes cast.

That brings us to the second question, what are the chances that the Democrats could win 53 percent of the Congressional vote in 2018?  Answering that question deserves an article unto itself.

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Technical Appendix: Seats and Votes in the 2018 Election

I am extending the simple model I presented in 2012 relating the proportion of House seats won by Democrats against that party’s share of the (two-party) national popular vote for Congressional candidates.  It uses dummy variables to represent each redistricting period (e.g., the 2000 Census was used to redistrict elections from 2002-2010), and a slope change that starts with the Republican House victory of 1994.

To review, the earlier model showed this pattern of partisan advantage for elections conducted since 1940:

The results for the 2010 redistricting were based solely on the 2012 election.  As we’ll see in a moment, adding in 2014 and 2016 only made that result more robust.

As I argued earlier, not all of this trend results from partisan gerrymandering.  Americans have sorted themselves geographically over the past half-century with Democrats representing seats from urban areas and Republicans holding seats from suburban and rural areas.  As partisans self-segregate, the number of “safe” seats rises, and electoral competitiveness declines.

Partisan self-segregation also makes gerrymandering easier.  Opponents can be “packed” into districts where they make up a super-majority.  House Minority Leader Nancy Pelosi routinely wins 80 percent or more of the voters in her tiny, but densely populated San Francisco district.  Many of these seats are held by minority Members of Congress because of our national policy of encouraging “majority-minority” districts.   These efforts were well-motivated as a response to racist gerrymandering that would “crack” minority areas and distribute pieces of them in a number of majority-white districts.  Unfortunately for the Democrats these policies have meant that too many of the party’s voters live in heavily-Democratic districts.

Here is the result of an ordinary least squares regression for the share of House seats won by the Democrats in elections since 1940:

If I plot the predicted and actual values for Democratic seats won, the model unsurprisingly follows the historical pattern quite closely:

The Democrats routinely won around sixty percent of House seats between 1940 and 1992.  Since then they have only held a majority in the House twice, in 2006 and 2008.  Notice, too, that both the actual and predicted values for 1994 to the present show much less variance than the earlier decades.  The results above show that the “swing ratio” relating seats and votes has become much smaller falling from 1.92 before 1994 to 1.33 (=-0.59+1.92) since.  A smaller swing ratio indicates that House elections have become less competitive since Bill Clinton was elected President in 1992.  Changes in vote shares are still amplified in seat outcomes, as they are in all first-past-the-post electoral systems like ours, but the effect has been diminished because of the increase in the number of safe seats on both sides of the aisle.

We can use this model to estimate the share of votes required in order for the Democrats to win a majority in the House.  This chart shows the predicted relationships between seats and votes for two historical periods, one through the election of Bill Clinton in 1992, and the other beginning with the Republican victory in the House election of 1994 under Newt Gingrich and his “Contract with America.”

The slope in the latter period is substantially flatter than in the earlier period, meaning that Congressional elections have become somewhat less competitive since 1992.  Changes in vote shares have a smaller effect on changes in seat shares than they did before 1994.

Finally, the third line represents an estimate for the relationship in 2018, using the 1994-2016 slope and only the post-2010 intercept shift.  The chart shows that for the Democrats to win half the seats in 2018 they will need to garner a bit over 53 percent of the two-party popular vote for the House.

*The intercepts in these charts represent weighted averages of the adjustments for the various Census years. For instance, the 1994-2016 line includes the coefficients for the 1990, 2000, and 2010 Census weighted by the number of elections in each decade. So in this case the 1990 and 2000 adjustments would have weights of five, and the 2010 adjustment a weight of three. The 2018 line applies only the 2010 redistricting adjustment.

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