That is the finding of an important new paper co-authored by one of the leading social science experts on districting, Professor Jowei Chen. In recent years, a debate has been taking place over whether it is particularly aggressive Republican gerrymandering in the 2010 round of redistricting or increasing geographic sorting of voters by partisan affiliation that explains the Republican “advantage” in the House — the fact that Republicans gain a larger percentage of House seats than their nationwide share of votes in House elections.

Chen and David Cottrell frame their inquiry as an effort to answer how many seats each party would control in the complete absence of gerrymandering. I won’t explain their full methodology here, but it basically consists of doing hundreds of computer simulations to measure the election results in differently designed districts, in which the building blocks are election-return results from the 2008 presidential election, all the way down to the Census block level. The computer is then told to start randomly at different points in the state and design equally populated, geographically continuous, and compact districts. The simulations do not take partisan or racial information into account. This method of using thousands of computer simulated districting plans based on objective criteria is increasingly being offered by experts, including Chen, in litigation.

Their bottom line finding is that if congressional “districts were drawn randomly with respect to partisanship and race, Republicans would only expect to lose a single seat in Congress to the Democrats.”

They do find that there are modest partisan gains from gerrymandering in individual states. But the gains to each party cancel out, in their analysis. Thus, they find that Republicans gain about five seats in states in which they controlled the redistricting process in this cycle. In states Democrats controlled, they gained about three seats. And once race is taken into account through the way the requirements of the VRA pre-clearance process demanded preservation of VRA districts, the Democrats gained another 1.75 seats compared to what a process based just on contiguity, compactness, and equal population would tend to produce.

This is certainly not the last word on this important subject. Any complex study of this sort poses many methodological issues. And their findings for congressional districts do not necessarily mean that gerrymandering has not made a significant difference for state legislative elections. But this study provides one of the most important counters to the argument that partisan gerrymandering plays a major role in the current composition of the House.

Further debates and discussions of this issue, including in the media, are going to have to take account of this important new analysis. It is consistent with what at least some other social scientists, using different approaches, have also concluded about the limited effects of gerrymandering on the composition of the House.