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.

Gerrymandering: The Final Reckoning

Over the past few posts I have narrowed down the list of states where we might claim gerrymandering affected the outcome of the 2012 Congressional election.  There is still one more task remaining — identifying those states where the partisan composition of the legislature and governorship, and the laws governing redistricting, enabled one party or the other to draw lines in a favorable manner.  This table combines information on each state’s constellation of partisanship and the method by which the state allocates Congressional seats.

There are four types of apportionment methods identified by Ballotpedia.  Most states place control over redistricting in the hands of the state legislature with the governor having a veto in all such states except North Carolina.  Nine states use nonpartisan commissions, and another five states can appoint a commission if the legislature fails to agree on a plan.  I treat those states as equivalent to states where the legislature is entirely in control.  Iowa reverses the backup system, with the legislature brought in only if the commission fails to come up with a plan.  I consider Iowa a commission state.

In the table above, I have divided the states into four groups.  At the top we have the eight states with unified Democratic control of state government and laws that grant the legislature and governor control over the apportionment process.  Some of the states identified in the last post as showing a pro-Democratic bias in their seat allocations like Massachusetts and Connecticut appear on this list of states with conditions favorable to Democratic gerrymandering.

Then follows a much larger group of states, nineteen, which had unified Republican state houses with control over redistricting.  Again we see some familiar faces from earlier tables like Pennsylvania and Ohio.  The third block of fourteen states have more uncertain gerrymandering conditions because of split partisan control either within the legislature or between the legislature and the governor.  The last group of nine states rely on nonpartisan commissions to draw their lines.  Both California and Arizona appear on this list despite showing a Republican and a Democratic excess of seats respectively.

So the last step is to combine the earlier list of states where gerrymandering might have taken place with the lists of states in the top two groups of the table above where the arrangement of political forces in the state might have encouraged gerrymandering.

Democratic Gerrymanders

Four of the eight states with pro-Democratic seat outcomes seem likely candidates for gerrymanderers.  All told, the Democrats probably won between four and six additional seats in Massachusetts, Connecticut, Illinois, and Maryland than they would have under a fair allocation of seats.  Gerrymandering seems much less likely to explain the additional Democratic victories in Georgia and Maine, where the Republicans were in control of the apportionment process, or in Arizona where district lines are drawn by a commission.

In Georgia, the entire process was controlled by the Republicans and was expected to produce a result favorable to that party.  However one of the targeted Democratic incumbents, John Barrow, moved after his district was redrawn, contested the 12th CD, and won with 54% of the vote.  Barrow’s dogged pursuit of his seat probably accounts for the “extra” Democrat in the Georgia delegation.

In New Hampshire, a Republican legislature faced off against a Democratic governor, though most of political struggles took place within Republican ranks.  Both seats had been captured from the Democrats in 2010, and the two new incumbents squabbled over the small changes that needed to be made to balance the two districts population.  In the event both seats were retaken by the Democrats in 2012.  This Democratic surge in New Hampshire probably has much to do with the regional trends to the Democrats across New England,  and the efforts by the Obama campaign to mobilize Democratic voters in a swing state.

Republican Gerrymanders

Two states that showed a pro-Republican bias had lines drawn by a commission rather than the legislature, while in Virginia legislative control was split between a Democratic Senate and a Republican House.  That leaves ten states with unified Republican control that show evidence of gerrymandering.  At the top of the list we have Pennsylvania, Ohio, Michigan and North Carolina, all states that have been repeatedly cited by observers as being heavily gerrymandered in the Republicans’ favor.  Unfortunately these observers often tend to claim the Republicans maintained control of the House entirely by gerrymandering and neglect the effects of incumbency.

At one extreme gerrymandering might have given the Republicans seventeen more seats in the House.  That figure combines the minimal estimate for Democratic gerrymanders, four, with the maximal estimate for the Republicans of twenty-one. If those seventeen seats had been won by Democrats, they would have eked out a one-seat majority in the House.  To achieve that value, though, we have to assume that urbanism only exerted effects in the Democratic states and had no effects in the Republican ones.  The opposite set of assumptions leads to an estimate of gerrymandering effects of just eight seats for the Republicans, far too few to have changed the outcome in the House.

These results provide a lower- and upper-bound on the effects of gerrymandering.  The actual effects probably lie somewhere in between.  Perhaps about a dozen seats remained with the Republicans because of gerrymanders, hardly an insignificant number to be sure, but not sufficient to explain why the Democrats could not win control of the House despite winning a slight majority of the popular vote for Congress.

 

Accounting for Geography

Updated, November 24, 2012, with complete results for all seats except the NC 7th.

If seats in Congress were allocated in an unbiased fashion, the Democrats might have won as many as twenty additional seats than they did on November 6th and would have taken control of the House of Representatives with 221 seats.

Where did this large Democratic deficit come from?  Democratic politicians and left-leaning pundits point their fingers at partisan gerrymandering by Republican state governments elected in the off-year landslide of 2010.  Students of the redistricting process itself point to a more fundamental problem for the Democrats, the geographic distribution of their supporters.

In an intriguing paper based on a careful simulation model of the redistricting process, political scientists Jowei Chen and Jonathan Rodden show that the tendency for Democratic voters to be tightly clustered in urban areas naturally advantages the Republicans when lines are drawn:

We show that in many urbanized states, Democrats are highly clustered in dense central city areas, while Republicans are scattered more evenly through the suburban, exurban, and rural periphery. Precincts in which Democrats typically form majorities tend to be more homogeneous and extreme than Republican-leaning precincts. When these Democratic precincts are combined with neighboring precincts to form legislative districts, the nearest neighbors of extremely Democratic precincts are more likely to be similarly extreme than is true for Republican precincts. As a result, when districting plans are completed, Democrats tend to be inefficiently packed in homogeneous districts.

In another study of the 2012 redistricting Nicholas Goedert observes that measures of urbanization correlate with the degree to which the Democrats gain a smaller or larger share of seats than what their votes share would predict.  So before we join the critics in claiming Republican gerrymandering as the source of the Democratic seat deficit, we need to first consider the role of urbanism.

The Census Bureau defines two types of urban areas — “urbanized areas” which contain a minimum of 50,000 people, and “urban clusters” which contain between 2,500 and 50,000 inhabitants.  The Bureau provides detailed information by state for both these types of urban areas.  I have tested a variety of these measures of urbanism by adding them to the baseline logit model for Democratic seats and votes.  Typically the measures for urban clusters have no significant effect on either vote or seat shares, but the data for urbanized areas, places with at least 50,000 people, matter considerably.

To get a sense of how urbanized areas and urban clusters are distributed across the country I recommend looking at two maps on this page at the Census Bureau website. The map on the left displays the density of the urbanized areas and urban clusters.  We can easily identify the large urban conglomerates like the Northeast Corridor, Atlanta, Chicago, Houston, Los Angeles, and Seattle. The second map codes entire counties and shows how California’s geography differs from most of the rest of the nation. Whole counties stretching back to the Nevada border are counted as urbanized even though most of the population living in the urbanized areas are along the coast.  California also dominates the list of urbanized areas when they are sorted by population density.  Of the top-thirty urbanized areas ranked by population density only six are outside California.

It is certainly the case that Democrats do better in states with a larger percentage of their populations living in urbanized areas.  About fourteen percent of the variation in Democratic Congressional vote across states can be accounted for by the proportion living in urbanized areas.  When it comes to the relationship betweens seats and votes, however, simply measuring how urbanized a state is does not affect the share of seats a party receives.  What turns out to matter much more is the population density of urbanized areas.  Adding that variable to our simple seats and votes model significantly improves our ability to predict the share of Democratic seats in a state given their share of its votes.  It also makes theoretical sense that urban density should play an important role given the relationship between clustering and apportionment bias Chen and Rodden explore.

To see how urban density influences affects the distribution of Congressional seats, look at this table which  shows the expected Democratic share of the seats given different values of the predictors.

Look first at the 50% column.  Even if the Democrats win half the vote in a state, they can only be assured of winning half the seats in the most heavily urbanized states.  Even in states like Maryland or Texas, with levels of urbanism higher than three-quarters of the states, winning half the vote does not guarantee a commensurate share of seats.  The effects of urban population density give the Democrats a boost in the most urbanized states, but they are few in number.  There are many more states where the Democrats need to poll well above 50% to claim half the seats in those states.

Given this powerful effect of urban density, I have rerun my seat estimates adjusting for the effect of urban density.  Not surprisingly, the Democratic deficit compared to the unbiased allocation shrinks when political geography is taken into account, but the amount of shrinkage is striking.

Let us start with the totals at the bottom of the table.  Using the method of “unbiased allocations” I estimate an 17 seat deficit for the Democrats in these states based solely on the share of the vote they won.  Adjusting for urban density accounts for fully 12 of those seats leaving a total deficit of just five.

Two of those five seats are in California, where a nonpartisan commission draws district boundaries.  As the maps above attest, the definition of “urbanism” applies rather differently to California than to the other states with densely populated urbanized areas.  So we might be a bit hesitant to claim that those two seats reflect gerrymandering.

Was Gerrymandering the Culprit? — Part I

Results updated on November 23, 2012, with final Congressional results for 434 races; NC 7th is still undecided.

It is now time to put some of the findings from earlier postings together and try to determine the extent of gerrymandering in the 2012 Congressional Elections.

Three factors should influence the number of House seats a party wins in a state Congressional election:

I have taken two separate measurements of the first item, the relationship between seats and votes.  I have calculated both a longitudinal measurement using elections from 1942 on, and a cross-sectional measurement using state results for 2012.  In both approaches I estimate the coefficients α and β of this “logit” model:

log(Democratic Seats/Republican Seats) = α + β log(Democratic Votes/Republican Votes)

The two models produce very different estimates for α, the seat “bias,” because it varies historically.  However the two estimates for β are nearly identical. The longitudinal estimate was 1.92; the cross-sectional estimate is 2.08.  For simplicity, I will just use two for the value of β.  (Mathematically, that implies that the ratio of Democratic to Republican seats varies in proportion to the square of the ratio of their votes.)

In this Technical Appendix, I explain why, if the Democrats win exactly half the vote, the only way they can win exactly half the seats is if the “bias” term α is zero. We can use this fact to create an “unbiased” distribution of seats.  I simply substitute two for β and apply it to the logit of the state-wide Democratic vote for Congress.  I will call this the “unbiased allocation.”  For each state I compare this estimate to the number of seats the Democrats actually won. Here are the results:

I have included all states where the difference between the predicted and actual number of Democratic seats was at least 0.7.  The state that gave us the word “gerrymander,” Massachusetts, shows the largest pro-Democratic deviation.  While the unbiased allocation model would award the Democrats only seven or eight of the nine seats in that state, not one Republican represents the Commonwealth of Massachusetts in Congress. The other state where Democrats did better than expected is Arizona, where they won a majority of the state’s Congressional seats with a minority of the popular vote.  Arizona had two of the closest races in the country, and they both fell to the Democrats by slim margins. All told, eight states including four New England states, have new Congressional delegations with an “extra” Democratic member in their numbers.

Many more states deviate from the unbiased allocation on the Republican side, with half-a-dozen states showing a pro-Republican bias of two, three, or, in the case of Pennsylvania, four seats. All told, sixteen states met our 0.7 criterion.  Compared to an unbiased allocation, the results in these sixteen states probably cost the Democrats 28 seats.  When we subtract out the eight extra seats the Democrats won in the pro-Democratic states, we get a net Democratic deficit in 2012 of some twenty seats compared to an “unbiased” allocation based solely on the popular vote for Congress in each state.

Before we start attributing all those seats to Republican gerrymandering, we first need to consider what other factors might influence the translation of Democratic votes to Democratic seats.  There is good reason to believe that the geographic distribution of Democratic voters by itself creates a pro-Republican bias when district lines are drawn.

 Accounting for Geography

 

The New Republican Bulwark in the House


For only the third time since 1940, the winner of the national popular vote for Congress failed to take control of the House of Representatives.  The Democrats won a slim majority of the (two-party) vote, 50.2%, but failed to gain back the House, winning just 197 of the 431 seats currently decided,* or 45.7%. This is the largest adverse gap between the Democratic Party’s share of seats and its share of votes since the New Deal.

For most of the years between 1942 and 1994, the Democrats enjoyed a “bonus” in terms of the seats they were awarded in the House of Representatives.  A good portion of that bonus came from the workings of our electoral system.  Political scientists and statisticians have long known that the method of voting used in Congressional elections, called “plurality voting” or “first-past-the-post,” exaggerates the size of majorities in the elected assembly.  A party that wins 51% of the vote gains more than 51% of the seats, and the bonus increases as the party’s share of the popular vote grows.** This is not a uniquely American phenomenon; we see the same exaggeration at work in countries like the United Kingdom which also employ plurality voting.  The bonus is quite evident if we plot the share of seats won by the Democrats against their share of the (two-party) popular vote.

The actual relationship between seats and votes is much steeper than the “parity” line which awards a party a share of the seats equal to its share of the vote.  Much of the Democratic advantage we saw in the first graph reflects this feature of our electoral system.  In the time-series plot we see the Democrats winning dramatically oversized House majorities in 1974 and 1976, but in the context of this historical relationship between seats and votes, those elections are not out of line.

I will use this relationship between seats and votes to see how Congressional reapportionment shifted the balance of power in the House.  The long-term relationship gives us a method for estimating how many seats the Democrats should have won given their share of the popular vote.  We can then look at the differences between these estimates and the actual share of seats won to measure any partisan bias.

Reapportionment by itself can change the partisan balance of the House.  As populations shifted from the Northeast to the Southwest, the fixed size of the House at 435 Members meant that seats in Democratic bastions like Massachusetts and New York were transferred to Republican strongholds like Texas.

What draws more attention from citizens and pundits alike is the possibility of partisan gerrymandering.   American political institutions grant parties enormous power to mold the structure of electoral competition.   Every ten years Constitutionally-mandated reapportionment requires state governments to redraw the boundaries of Congressional districts.  Nine states use a nonpartisan commission to draw district lines.  Of the remaining 41, the state legislature and governor have full control of the redistricting process in 28 of them.  The other thirteen states use a “hybrid” approach with a commission that is usually subservient, and sometimes purely advisory, to the elected state legislature.

These institutions invest an enormous amount of power in one specific set of state legislators and governors, those elected in a year ending in zero.  These partisan elected officials have the power to structure competition for the House of Representatives for the decade to come.  The development of sophisticated computer software combined with geographic marketing databases places enormous power in the hands of determined modern gerrymanderers.

One way we might begin the measure the extent of partisan gerrymandering is to look at whether individual “apportionment periods,” the five elections conducted in the same seat boundaries, showed a bias toward one party or another.  We can use the seats/votes relationship to provide a baseline expectation of what seat outcomes ought to be, then calculate the average deviation for each five-election apportionment period like this.

I date apportionment periods by the date of the Census, so the 1940 apportionment covers elections held from 1942 through 1950. The vertical bars measure the difference between the average number of seats the Democrats won in the five Congressional elections following each Census and the number of seats they “should” have won in that period based on their share of the popular vote.  Remember that this technique already accounts for the bonus resulting from our plurality-voting electoral system.  These bars measure any additional partisan bias associated with a particular apportionment period.

The electoral system showed a distinct pro-Democratic bias of five to eight seats for most of the period between the New Deal and the 1990s.  The only exception came in the 1950s when the bonus fell to an estimated two seats, a value not statistically different from zero.  The Democrats’ bonus began to slip after 1960 and has moved in the Republicans’ direction ever since.  Extrapolating the pro-Republican trend from 1960 through 2010 would predict an advantage for the GOP of about three or four seats in 2012. The actual Republican bias in 2012 looks closer to ten seats.  Not an auspicious start to the decade ahead if you are a Democrat.

While many commentators have pointed to Republican gerrymandering as the primary explanation for this result, I want to take things a bit more slowly and consider first how the process of reapportionment itself may have altered the balance of power in the House by shifting seats from Democratic states to Republican ones.  I begin that discussion in the next post.

The Effects of Reapportionment

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*I awarded two of the six undecided House races from the November 12th list at CNN. I gave both AZ 9 and FL 18 to the Democrats, leaving two races in California, and one each in Arizona and North Carolina as undecided. That puts the current tally at 234 to 197 in favor of the Republicans. All four of these uresolved contests show slim majorities for the Democrats.  If they took all four it would raise their total to 201.  Even with those seats added, that’ hypothetical mark of 46.2% of the seats would remain the worst result by a majority winner since the New Deal.  Both the 1942 Republicans and the 1996 Democrats failed to win the House, but they both won a larger share of the seats than the 2012 Democrats.  (Return)

**The claim that the bonus increases as the popular vote share increases holds true for values in the range observed historically.  Eventually the bonus must shrink as the popular vote approaches 100%.  In the historical period I am examining here, the Democrats never won less than 45.3% of the popular vote (1946) or more than 58.3% (1974). (Return)