Spurious majorities in the US House in Comparative Perspective

In the week since the US elections, several sources have suggested that there was a spurious majority in the House, with the Democratic Party winning a majority–or more likely, a plurality–of the votes, despite the Republican Party having held its majority of the seats.

It is not the first time there has been a spurious majority in the US House, but it is quite likely that this one is getting more attention ((For instance, Think Progress.)) than those in the past, presumably because of the greater salience now of national partisan identities.

Ballot Access News lists three other cases over the past 100 years: 1914, 1942, and 1952. Sources disagree, but there may have been one other between 1952 and 2012. Data I compiled some years ago showed a spurious majority in 1996, if we go by The Clerk of the House. However, if we go by the Federal Election Commission, we had one in 2000, but not in 1996. And I understand that Vital Statistics on Congress shows no such event in either 1996 or 2000. A post at The Monkey Cage cites political scientist Matthew Green as including 1996 (but not 2000) among the cases.

Normally, in democracies, we more or less know how many votes each party gets. In fact, it’s all over the news media on election night and thereafter. But the USA is different. “Exceptional,” some say. In any case, I am going to go with the figure of five spurious majorities in the past century: 1914, 1942, 1952, 2012, plus 1996 (and we will assume 2000 was not one).

How does the rate of five (or, if you like, four) spurious majorities in 50 elections compare with the wider world of plurality elections? I certainly do not claim to have the universe of plurality elections at my fingertips. However, I did collect a dataset of 210 plurality elections–not including the USA–for a book chapter some years ago, ((Matthew Soberg Shugart, “Inherent and Contingent Factors in Reform Initiation in Plurality Systems,” in To Keep or Change First Past the Post, ed. By André Blais. Oxford: Oxford University Press, 2008.)) so we have a good basis of comparison.

Out of 210 elections, there are 10 cases of the second party in votes winning a majority of seats. There are another 9 cases of reversals of the leading parties, but where no one won over 50% of seats. So reversals leading to spurious majority are 4.8% of all these elections; including minority situations reversals are 9%. The US rate would be 10%, apparently.

But in theory, a reversal should be much less common with only two parties of any significance. Sure enough: the mean effective number (N) of seat-winning parties in the spurious majorities in my data is just under 2.5, with only one under 2.2 (Belize, 1993, N=2.003, in case you were wondering). So the incidence in the US is indeed high–given that N by seats has never been higher than 2.08 in US elections since 1914, ((The original version of this statement, that “N is almost never more than 2.2 here” rather exaggerated House fragmentation!)) and that even without this N restriction, the rate of spurious majorities in the US is still higher than in my dataset overall.

I might also note that a spurious majority should be rare with large assembly size (S). While the US assembly is small for the country’s population–well below what the cube-root law would suggest–it is still large in absolute sense. Indeed, no spurious majority in my dataset of national and subnational elections from parliamentary systems has happened with S>125!

So, put in comparative context, the US House exhibits an unusually high rate of spurious majorities! Yes, evidently the USA is exceptional. ((Spurious majorities are even more common in the Senate, where no Republican seat majority since at least 1952 has been based on a plurality of votes cast. But that is another story.))

As to why this would happen, some of the popular commentary is focusing on gerrymandering (the politically biased delimitation of districts). This is quite likely part of the story, particularly in some sates. ((For instance, see the map of Pennsylvania at the Think Progress link in the first footnote.))

However, one does not need gerrymandering to get a spurious majority. As political scientists Jowei Chen and Jonathan Rodden have pointed out (PDF), there can be an “unintentional gerrymander,” too, which results when one party has its votes less optimally distributed than the other. The plurality system, in single-seat districts, does not tote up party votes and then allocate seats in the aggregate. It only matters in how many of those districts you had the lead–of at least one vote. Thus a party that runs up big margins in some of its districts will tend to augment its total in its “votes” column at a faster rate than it augments its total in the “seats” column. This is quite likely the problem Democrats face, which would have contributed to its losing the seat majority despite its (apparent) plurality of the votes.

Consider the following graph, which shows the distribution (via kernel densities) of vote percentages for the winning candidates of each major party in 2008 and 2010.

Click image for larger version

We see that in the 2008 concurrent election, the Democrats (solid blue curve) have a very long and higher tail of the distribution in the 70%-100% range. In other words, compared to Republicans the same year, they had more districts in which they “wasted” votes by accumulating many more in the district than needed to win it. Republicans, by contrast, tended that year to win more of their races by relatively tighter margins–though their peak is still around 60%, not 50%. I want to stress, the point here is not to suggest that 2008 saw a spurious majority. It did not. Rather, the point is that even in a year when Democrats won both the vote plurality and seat majority, they had a less-than optimal distribution, in the sense of being more likely to win by big margins than were Republicans.

Now, compare the 2010 midterm election, in which Republicans won a majority of seats (and at least a plurality of votes). Note how the Republican (dashed red) distribution becomes relatively bimodal. Their main peak shifts right (in more ways than one!) as they accumulate more votes in already safe seats, but they develop a secondary peak right around 50%, allowing them to pick up many seats narrowly. That the peak for winning Democrats’ votes moved so much closer to 50% suggests how much worse the “shellacking” could have been! Yet even in the 2010 election, the tail on the safe-seats side of the distribution still shows more Democratic votes wasted in ultra-safe seats than is the case for Republicans. ((It is interesting to note that 2010 was very rare in not having any districts uncontested by either major party.))

I look forward to producing a similar graph for the 2012 winners’ distribution, but will await more complete results. A lot of ballots remain to be counted and certified. The completed count is not likely to reverse the Democrats’ plurality of the vote, however.

Given higher Democratic turnout in the concurrent election of 2012 than in the 2010 midterm election, it is likely that the distributions will look more like 2008 than like 2010, except with the Republicans retaining enough of those relatively close wins to have held on to their seat majority.

Finally, a pet peeve, and a plea to my fellow political scientists: Let’s not pretend there are only two parties in America. Since 1990, it has become uncommon, actually, for one party to win more than half the House votes. Yet my colleagues who study US elections and Congress continue to speak of “majority”, by which they mean more than half the mythical “two-party vote”. In fact, in 1992 and every election from 1996 through at least 2004, neither major party won 50% of the House votes. I have not ever aggregated the 2006 vote. In 2008, Democrats won 54.2% of the House vote, Republicans 43.1%, and “others” 2.7%. I am not sure about 2010 or 2012. It is striking, however, that the last election of the Democratic House majority and all the 1995-2007 period of Republican majorities, except for the first election in that sequence (1994), saw third-party or independent votes high enough that neither party was winning half the votes.

Assuming spurious majorities are not a “good” thing, what could we do about it? Democrats, if they are developing a systematic tendency to be victims of the “unintentional gerrymander”, would have an objective interest in some sort of proportional representation system–perhaps even as much as that unrepresented “other” vote would have.