It's not all that unusual for results in a tight two-party race to be perverse, ie for the losing party in votes to win more seats. Well-known examples include the 2000 US Presidential vote, the first 1974 British election, the 1951 British election and (for us STV fans) the 1981 election in Malta. It is unusual for such a tight race to deliver a seat benefit to the losing party, and that is worth investigating further.
First of all, we should be clear that not all 435 seats were contested in a straight fight between Republicans and Democrats. 21 seats had only one candidate, and another 24 saw only one of the two main parties represented. Had there been a contest in every seat, the Democrats would I think still have been ahead in the national vote total, but even more narrowly, and of course it's a reasonable assumption that the seat total would have been the same. The proposition that the overall result did not really reflect the will of the voters survives the hypothetical challenge that too many seats were uncontested to tell, since the uncontested seats were fairly evenly split (25 Republicans, 20 Democrats). Having said which, 10% of seats being uncontested is not really a sign of a healthy democracy.
Looking at the 410 seats that were contested between the two parties, it becomes clear that there is some systematic disadvantage for the Democrats somewhere. In the 191 seats where they beat the Republicans, they averaged 67% of the vote; Republicans averaged only 61% of the vote in the 209 seats where they beat the Democrats. In other words, more Democrat votes were in areas where they had a large majority, and more Republican votes were in areas where they were comfortably smeared out to just beat the Democrats. On a uniform swing from this year's results, Democrats will need to lead the Republicans by more than 7% nationwide to win a majority in the House, which is a pretty colossal differential (and very unlikely to be achieved in 2014, given the tradition of mid-term swings against the White House).
The question is, to what extent is this an imbalance inevitable consequence of the geographical concentration of Democratic voters, and to what extent is it the result of human design? There are seven states where human design for the House is irrelevant because they elect only one representative (two Democrats and five Republicans). Looking at the other 43 states, there were 23 where Republicans got more votes and 20 where Democrats got more votes as a total in the state House races. Since the electoral districts are designed separately by each state (there is a handy table of procedures here) it's not all that surprising that the 23 states where Republicans won should over-deliver Representatives for the GOP, and that this has a greater effect than the 20 states which the Democrats won. However, the margin of the GOP victory remains surprising.
What is a bit more surprising is that there were five states where the 'wrong' party won, where despite winning fewer votes the party in question won more seats. They were Arizona, Michigan, North Carolina, Pennsylvania and Wisconsin.
In Arizona Democrats won 5 seats and Republicans 4, despite being behind by 43% to 53%, on boundaries drawn by a bipartisan independent commission.
In the other four states, Republicans controlled the redistricting process.
Wisconsin voted very narrowly for the Democrats, by 50.5% to 49.0%, but Republicans won 5 seats to the Dems' three. That is possibly a fluke which cancels out Arizona.
In Michigan, Democrats won 50,9% and Republicans 45,6%, but the GOP won 9 seats to the Dems' 5.
In North Carolina, Democrats won 50,6% and Republicans 48,9%, but the GOP won 9 seats to the Dems' 4.
In Pennsylvania, Democrats won 50,2% and Republicans 48,9%, but the GOP won 13 seats to the Dems' 5.
In those last three states, where the Republican control of redistricting delivered a large majority of congressional delegates despite a majority vote for the Democrats, the GOP won 31 seats and the Democrats 14, a difference of 17; that accounts for more than half of the congressional majority of 33 right away.
Republicans were also able to draw the boundaries to deliver a bigger majority of seats than their vote share would have indicated in Georgia, Indiana, South Carolina, Virginia, Texas, Florida and Ohio, and got clean sweeps of the nine congressional seats from Oklahoma and Kansas with vote shares in the lower 60s in each state. Against this one must set New Hampshire, where despite full Republican control of the process the Democrats won both seats by slender margins. One should also consider the states where Democrats controlled the process: they won all seven seats in Massachusetts on two thirds of the vote, and Illinois and Maryland both over-delivered on a substantial Democratic majority of the popular vote. However West Virginia returned two out of three Republicans, and Arkansas four out of four, suggesting that for whatever reason no successful gerrymander was implemented there by the Democrats.
I come away from this exercise not completely convinced that the Republicans owe their majority in the House to systematic gerrymandering, but that it certainly accounts for more than half of it, possibly much more. When you have a single-seat electoral system, it's not unusual even for fairly drawn seats to lead to a systematic imbalance in favour of (or more often against) particular parties. The creeping increase of constituencies in Wales, with consequent benefits for Labour, is my favourite example of this. However it is actually on the record that the seats in almost half of the 50 states are not fairly drawn, but designed for partisan advantage.
Just because gerrymandering may not have the decisive factor in the unequal outcome in the House vote doesn't mean it isn't a problem. I think it is a problem that gerrymandering is institutionalised; I think it is a problem that one race in ten is not contested by both major parties; and I think it is a problem if the election results fail to reflect the will of the voters.