How under-represented was the Conservative Party on 6 May? Oh sure, I know that the party was over-represented, relative to its vote share. But that’s what FPTP is supposed to do. In fact, it is supposed to do so sufficiently to give a “decisive” result. At least that’s what David Cameron said throughout the campaign in defense of the current electoral system. So, relative to the expectation of a substantial boost from FPTP, how under-represented was the largest party in the recent UK election?
By running the seat-vote equation on the actual voting result, we can get an idea of the answer to this question. The Conservatives won 307 seats, for 47.2%, on 36.1% of the vote. Labour came second with 258 seats, for 39.7%, on 29% of the vote. For these top two vote percentages, the seat-vote equation says the largest party “should have won” 51.4% of the seats and the second “should have won” 31.5%. (The Liberal Democrats presumably “should have” won the greater part of the remaining 17%, rather than the mere 9% that they have to show for their 23% of the vote.*)
For the largest party, obviously the deviation between an expectation of 51.4% and an actual result of 47.2% is minor, aside from the rather important detail of these percentages straddling the magic 50% (plus 1) marker.
The outcome of the election continues in a striking way the over-representation of Labour. Note that their 29% of the vote could have been expected to result in just over 30% of the seats, but instead they are close to 40%. The bias of the system in favor of Labour, whereby that party wins more seats than the Tories for any given vote share, is well known. It is likely not, however, a product solely of the current district boundaries, as Cameron and other Conservatives are fond of saying. Districting plans come and go, but this bias has been in place for some time.
We can see the differential treatment of the parties by looking at the advantage ratios (%seats/%votes). In this election, Labour had A=1.37, which is the best result for a second-place party in the UK in my data-set (which goes back to 1959). For the Conservatives, A=1.31. While this is a relatively low A for the largest party, in the UK context it is not low–for a first party branded as “Conservative.” Even when the Conservatives were winning substantial seat majorities from 1979 through 1992, their A surpassed 1.25 only in 1983 (1.44) and 1987 (1.37), while in the “Thatcher landslide” of 1979 it was only 1.22. (In 1992 it was 1.23.) Labour, on the other hand, enjoyed advantage ratios of 1.47 or greater in each of the three recent elections when it was the largest party.
These figures suggest that the Conservatives might have a hard time finding a FPTP districting plan** that would really work for them, unless they can again be confident of surpassing 38% or so of the vote. Meanwhile, Labour is benefiting rather handsomely from FPTP, though the 2010 outcome in particular suggests that the bulk of that advantage is coming at the expense of Britain’s rather large third party instead of the Conservatives.
* Various fourth and lower-ranked parties won around 4% of the seats, owing to concentration of the relative few votes won by any one of them, despite combining for 11.9% of the vote. We can discount them for present purposes and just call them “others.” (Which is not to say that some of them might not prove relevant in the coming parliament, of course.)
** That is, without major gerrymandering on a scale not practiced in the UK, unlike the USA.