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The Seats/Votes Relationship in the U.S. House 1972-2018

Editor’s Note: This is an updated version of a story we previously published in June 2015 and January 2017 looking at the national House vote.


— After adjusting the results for uncontested races, Democrats won the national House popular vote by about seven percentage points last fall.

— The size of the Democrats’ national win allowed them to translate their share of the vote into a roughly approximate share of seats.

— House maps in the 1970s and 1980s exhibited a pro-Democratic bias; more recently, the map has had a pro-Republican bias.

The relationship between seats and votes in the 2018 House race

Redistricting in the U.S. House of Representatives is not a unified process as is the case for most national legislatures, but the result of the cumulative actions in the states that have more than one representative. Nevertheless, it is useful to look at the entire House to see how the decisions in the states combine to form a fair or biased playing field for the parties.

One commonly used method for analyzing the partisan nature of the redistricting process is the seats/votes relationship (see here for a longer discussion). For this analysis, simple least squares regression is used to relate the percentage of the two-party votes that the Democrats received compared to the percentage of the seats they won. The Pearson’s R2 tells us how strongly the allocation of seats is related to the votes received by each party. The slope of the regression line is called the swing ratio, and it tells us how responsive the system is to changes in the vote. One can determine partisan bias by simply solving the regression equation for the situation in which the Democrats received 50% of the votes. At that level, they should also receive about 50% of the seats if the playing field is level.

Determining the percentage of the two-party votes received by Democratic candidates for the House requires attention to two questions. The first question is how to count elections in states that have majority vote requirements with runoff elections after November (e.g., Louisiana), and elections in which all the candidates in the November general election are in the same party as a result of a jungle-primary system (as can sometimes happen in California and Washington). If the candidates in the final election are both in the same party, I counted the contest as unopposed for that party. If there was a runoff after November, I combined the vote of each party’s candidates in the November election.

A second question is what to do with these and other contests that lack two-party competition. I define an opposed contest as one in which there was both a Republican and a Democratic candidate in the November election on the ballot. If the vote in unopposed contests is included, the total for the party that had the most unopposed candidates is inflated, because their opponents would have received at least some votes. If the vote of the unopposed candidates is excluded, the vote of the party with the most unopposed candidates is understated because unopposed candidates would undoubtedly receive a substantial majority of the votes if they were opposed.

One way to deal with this problem is to substitute the vote of some other set of candidates in districts where the congressional candidate is unopposed. But on a nationwide basis the only office available for that job is the presidency, and that is only available in half the congressional elections because the House is elected every two years while the presidency is only elected every four years. Moreover, this is exactly the wrong office to use. There is great variation in presidential and congressional voting. Votes for U.S. Senate or governor could be substituted into unopposed races, but this also has problems. Voters typically know more about candidates for these offices, only about a third of the states have a Senate election in any year, almost all the governors now have four-year terms, and a majority of gubernatorial races are now decided in midterm years.

My solution is to estimate the vote that each party would receive in unopposed contests and add this to the vote in the opposed races. The formulas for the adjustment of the vote for each party is:

d = x + amv + bm(1 – v)

r = y + bmv + am(1 – v)


d = estimate of Democratic vote

r = estimate of Republican vote

x = vote for all opposed Democratic candidates

y = vote for all opposed Republican candidates

a = number of unopposed Democratic candidates

b = number of unopposed Republican candidates

m = mean number of votes cast for both Republican and Democratic candidates in opposed contests

v = proportion of the vote that unopposed candidates would have received if they had been in an opposed contest

The two-party voter turnout in unopposed districts is assumed to be equal to the mean turnout in opposed contests. This is designated as “m” in the formula.

Congressional elections expert Gary Jacobson estimates the percentage of the vote that we would expect unopposed candidates would have received, on average, if they had been opposed (v in the formula) at 71% with a standard deviation of 10%. His analysis is based on the support that congressional candidates received in the election following or preceding the one in which he or she was not opposed.

With this calculation, I derived the percentage of the two-party vote that the Democrats would have received if all contests were opposed in recent elections. These figures deviate little from total vote without this adjustment. For example, in 2018 the unadjusted total was 54.36% Democratic, while the adjusted vote was 53.49% Democratic. Over the years I have collected the data from a variety of reliable sources, most commonly the Clerk of the U.S. House. The data for 2016 and 2018 come from the Cook Political Report.

The logical place to start the analysis is with the 1972 election, which is the beginning of the first full redistricting cycle after the U.S. Supreme Court required congressional districts to be one-person-one-vote. In the period from 1972 to 2018, only in 1996 and 2012 did the party that received the most adjusted votes fail to receive the most seats in the House. In 1996, the Democrats received 50.02% of the two-party vote (adjusted), but failed to retake the House from the Republicans. In 2012, the Democrats received 50.6% of the two-party vote, but again failed to retake the House.

Given the power of incumbency, the “out” party may need to get well over 50% of the two-party vote to take over the house even if there is no gerrymandering. The Republicans received 54.5% of the two-party vote in 1994 to take over the House, and the Democrats took it back in 2006 with 53.9%. The Republicans took it back again in 2010 with 52.9%. But the GOP lost it again in 2018 when the Democrats received 53.5% of the vote.

Table 1 shows the number of unopposed contests for both parties in each election since 1972. In general, the party with the most momentum going into the election period had the largest number of unopposed contests, as one would expect. This relationship was greatly exaggerated in 2018. The Republicans only had three unopposed contests this year, while the Democrats had about the same number as previously: 38. The number of unopposed Democrats has been going down as the Republicans first became competitive in the previously one-party Democratic South and then became dominant there. The number of unopposed Republicans has been going up over time mainly as a result of those same changes in the South.

Table 1: Number of unopposed Democrats and Republicans running for Congress 1972-2018

Table 2 shows the correlation, slope, and bias figures for the entire period and for each recent redistricting cycle. Figure 1 shows a scatterplot of this relationship during the entire period from 1972 to 2018, and Figure 2 shows the relationship during the 2012 to 2018 period. The Pearson correlations indicate that the allocation of seats is consistently related to the votes cast. For this entire period, the swing ratio has been appropriately at or above 1.0, indicating adequate response to changes in the vote. Over the entire period, the system has had little partisan bias — a Republican advantage of only 0.2%, which is perhaps an additional one seat if the vote were evenly split. However, in the 1970s and 1980s, the Democrats had a sizable advantage, while in more recent elections this advantage has shifted from a very slight Democratic bias in the 90s to a Republican advantage starting in 2002. Thus, the overall fairness statistics disguise substantial variation over several different redistricting cycles.

Table 2: Statistics on seat/vote relationship 1972-2018

Figure 1: Scatterplot of Democratic percentage of the two-party adjusted vote to Democratic percentage of the seats in the House won 1972-2018

Figure 2: Scatterplot of Democratic percentage of the two-party adjusted vote to Democratic percentage of the seats in the House won 2012-2018

The 2012-2018 elections show an enlargement of this Republican bias. If the vote were evenly split, the Democrats would get only 46.6% of the seats on average (202 seats out of 435). This pretty well describes what has been happening during this decade. In 2012, the Democrats received 50.6% of the votes (adjusted), but only 46.2% of the seats. In 2014, the Democratic percentage of the adjusted votes declined to 47.6%, and they won only 43.2% of the seats. In 2016, the Democrats did slightly better with 49.2% of the votes, but still won only 44.6% of the seats. In 2018, however, the Democratic candidates received 53.5% of the votes and won 235 seats (54.0%). (I counted the still-undecided seat in North Carolina as going to the Republicans and included the preliminary vote for that office.) Some mid-decade redistricting (especially in Virginia and Pennsylvania) seems not to have affected the overall pattern for the current cycle.

Using the regression equation for the 2012-2018 cycles, the Democrats in 2018 should have received 53.1% of the seats (231 seats) because they received 53.5% of the vote. So the Democrats did four seats better than expected.

The more recent Republican advantage may be due, in part, to the requirements of the Voting Rights Act (VRA) to create majority-minority districts, thus artificially packing the most reliable Democratic voters in a few districts. The high point of this requirement, however, was in the 90s, when there was almost no partisan bias. Thus, the VRA is not inconsistent with unbiased redistricting or even a pattern that has a small Democratic bias. To some extent, the bias may derive from the way in which Democratic and Republican voters are concentrated geographically, and not with the implementation of the Voting Rights Act per se. It is clear, however, that one cause of the current bias must be gerrymandering in several large states by Republican state legislatures and governors in the redistricting cycle following the 2010 census.

Theodore S. Arrington is Emeritus Professor of Political Science at the University of North Carolina at Charlotte. He has been an expert witness in over 40 voting rights cases in the United States and Canada, and his commentary is frequently cited in the press.