Redistricting the U.S. House of Representatives is not a unified, national process, unlike most national legislatures. Rather, it’s the result of cumulative actions taken by individual states. Nevertheless, it is useful to look at the entire House to see how the decisions in the states combine to form a fair or an unfair playing field for the parties.

The most common method for analyzing the partisan nature of the redistricting process is the seats-votes relationship. For this analysis, a simple regression is used to relate the percentage of the two-party vote that the Democrats received to the percentage of the seats that 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 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 Louisiana and Texas, which have majority vote requirements, and elections in which all the candidates in the general election are in the same party, as can occur in a new system used in California. If the candidates in the final election are both in the same party, I counted the contest as unopposed for that party.

A second question is what to do with these unopposed contests. I define an opposed contest as one in which there was both a Republican and a Democratic candidate. 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 House seats are elected once every two years while the presidency is elected once 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 33 or 34 of the states have a Senate election in any year, and nearly all governors now have four-year terms.

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)

Where:

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 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.

Gary Jacobson of the University of California, San Diego 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 received in recent elections. These figures deviate little from other measures of the “total vote” without this adjustment.

The logical place to start the analysis is with the 1972 election, which is the beginning of the first redistricting cycle after the U.S. Supreme Court required congressional districts to be one person, one vote (the Supreme Court is now reconsidering the meaning of this standard). In the period from 1972 to 2014, 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 GOP. 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%.

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. In 2014 both parties had about the same number of unopposed contests: 41 for the Democrats, 36 for the Republicans. In this situation, my adjustment procedure makes little difference in the Democratic percentage of the two-party vote.

Table 1: Number of unopposed Democrats and Republicans running for Congress, 1972-2014

Table 2 shows the correlation, slope, and bias figures for the entire period and for each recent redistricting cycle. 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 Democratic advantage of only 0.1%, which is perhaps an additional one seat if the vote were evenly split. At the beginning of this period the Democrats had a sizable advantage, but in more recent elections this advantage has shifted from a slight Democratic bias in the 90s to a somewhat larger Republican advantage starting in 2002.

Table 2: Statistics on seat-vote relationship, 1972-2014

Note: *Preliminary figures with only two data points

The 2012 and 2014 elections show an enlargement of this Republican bias. If the vote were evenly split, the Democrats would get only 46% of the seats on average (200 seats out of 435). The adjusted seat-vote figures for these two elections confirm the pattern. 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 43.2% of the seats. The Democrats would need to get 55% of the adjusted vote to win a majority of the seats, and that may not include any additional vote that would be necessary to overcome the larger number of Republican incumbents. This level of Democratic dominance is not impossible, but unlikely. The Democrats received more than 55% of the adjusted vote only in 1974, 1976, and 1982.

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 1990s. Thus the VRA is not inconsistent with unbiased redistricting or a pattern that retains a small Democratic bias. One cause of the current bias is gerrymandering in several large states that Obama won in 2008 and 2012, but that were redistricted by Republican state legislatures and governors in 2011 and 2012 after GOP success in the 2010 election cycle.