How far off the seat-vote equation was the UK 2010 result?

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.

13 thoughts on “How far off the seat-vote equation was the UK 2010 result?

  1. I agree completely, but there’s another way of looking at it.

    This year, the Conservatives scored a seven percent popular vote advantage but fell twenty seats short of an absolute majority. However, a slightly larger 7.5% lead in 1992 yielded an overall majority of 21 for John Major, while in 1979 an identical seven percent advantage gave Margaret Thatcher a majority of 43. Finally, in 1959 Harold Macmillan remained in office with an overall majority of 100 on a popular vote lead of just 5.6%, while Labour won the same number of seats as earlier this month – namely, 258 – but this time around with just 29% of the vote, as opposed to 43.8% over a half-century ago.

    To paraphrase the late Earl of Stockton, the Conservatives never had it so good with FPTP: it’s been diminishing returns for them ever since – and redistricting (or rather, boundary review as the British would have it) is not the solution.

  2. Could the effect described above be due to increased concentration of the Conservative vote in the Home Counties and other parts of the Southeast?

  3. Only to a certain extent, Ed: as I’ve previously noted in a comment here, the Conservatives are now just 0.6% behind Labour throughout northern England and the Midlands, yet Labour retained a sizable 37-seat lead (14.1% of 262 seats) over the Tories in that part of the U.K.

    The bias in the electoral system appears to be mainly driven by differences in turnout between Labour- and Conservative-held constituencies. Using the results published by the Press Association on its election website (available in Excel format on my website’s U.K. page), turnout in the 258 constituencies won by Labour was significantly lower (61.2%) than in the 305 constituencies won by Conservative candidates (excluding the Speaker), where it reached 68.3%. In fact, the average vote for winning Labour candidates was 19,383, while for Conservatives elected to the House of Commons the figure rose to an average of 23,866 votes.

    Moreover, Labour-held constituencies tend to be slightly smaller than their Tory counterparts: the former had an average of 68,405 electors, while in the latter the figure increased to 72,477; the average electorate size for the entire U.K. – excluding Thirsk and Malton, which votes next week – stood at 70,167. (Incidentally, for northern England and the Midlands only, the average electorate size differences are even smaller.)

    In other words, Labour needs fewer votes than the Conservatives to win constituency seats, and that phenomenon introduces a bias in the electoral system, which skews the distribution of seats in favor of Labour.

  4. I think a more likely reason is that the UK has extraordinary slow boundary reviews for some reason. District population is only one of a set of conflicting criteria for redistribution. The boundaries commissions regularly take years to complete a redistribution and work from a set of conflicting criteria. The process is just incompetent.

    Part of the problem is the incompetent way the UK updates its constituency boundaries. Most of the 2005 boundaries were based on the 1990 electoral rolls, ignoring 15 years of flight from inner cities that has seen Labour-leaning constituencies electing MPs with many fewer voters than other seats.

    Even the so-called “new boundaries” used in May are a decade out of date. The UK held only six boundary reviews in the 20th century, whereas Australia has one very five years. Australia also uses accurate census figures.

    I think it likely that the various biases are as much random as reflecting demographic shifts, and that interpreting them may suffer from gambler’s fallacy.

  5. Quote of the week for me was George Osborne explaining how David Cameron’s new (coalition) government was going to take firm, decisive action to restore Britain’s public finances after their depletion over 13 years by Labour’s willpowerless (three landslide absolute majority) governments.

  6. The ultimate deviation from the seat-vote equation is the wrong-winner election. I thought I’d heard all the worst “wrong-winner” horror stories . . . but I missed the worst one of all.

    In South Africa the 1948 elections saw the National Party defeat the ruling United Party on a platform of imposing “Apartheid.”

    In 1948, 1953 and 1958 the more moderate United Party got more votes than the National Party, but the National Party won all three times.

    Apartheid was the fruit of First-Past-The-Post.

  7. ‘… [Professor] John Curtice … suggests that this most recent election ought not to be considered a freakish result and that even if the voting system remains unaltered hung parliaments are probably as likely as not for the foreseeable future. If that’s the case – and even with redrawn constituency boundaries it seems quite probable that at least some of the factors he mentions (the decline in the number of true marginals, the way the Lib Dem vote is spread and so on) will continue to nudge parliament towards a hanging.

    If we accept that this is the case then the argument in favour of treating the Liberal Democrats well – and granting them greater influence than their weight of parliamentary numbers might indicate appropriate – is strengthened still further. Because it’s not just about this government, it’s also a question of future governments. If – a mighty if for sure but stick around – this partnership goes well, it will be much easier to form Tory-Liberal ministries in the future. Conversely, if it ends badly (most probably on account of Tory arrogance or insensitivity) then such efforts will be made more difficult than might otherwise be the case. Memories of the Camerlegg Ministry will become exceedingly important and, I warrant, much more important than many MPs of either party imagine right now.

    Nevertheless, if Curtice [… is] right and hung parliaments become more common than they have been in the past as we continue to try and squeeze three parties into a system designed for two then the prize becomes getting to dance with the Liberal Democrats more often than the competition…’

    – Alex Massie, “Loving the Liberal Democrats in a Hung Britain”, The Spectator (25 May 2010)

  8. Great quote from Massie; Curtice is right. The system has been trending towards non-majority situations for a while. In fact, the seat-vote equation says there should have been a minority situation in 2005, because the equation does not know about the partisan bias in favor of the Labour party (i.e. that it almost always outperforms its expectations in the votes-to-seats conversion process).

  9. I recall reading a British pamphlet – circa 1988, ie about Year 12 Before Internet – published by either Charter 88 or the Campaign for Fair Votes, that FPTP was going to frack up in the UK eventually because “the British electorate is regionalising” (of which I suppose tactical voting is one side-effect). In hindsight, this was masked because in all UK Commons elections since 1974b the party with most votes had a fairly wide lead over the second-highest, even if the absolute percentage was well below 50% (or even 45%).

    I wonder, idly, if the rise in tactical voting can be attributed to (a) an increase in political literacy among the demos, and (b) the Internet greatly reducing the transaction costs for arranging vote-swaps.

    As to (a), in the 1980s it was not uncommon to hear Australian voters warning that you’d “waste your vote” if you put [1] for the Democrats or the DLP. In the last few years, this sort of psychological illiteracy seems to have declined and the average punter has some idea that preferences change thing (even if, as I suspect, many think they do so via a points system something like Nauru’s). So I wonder if susceptibility to the opposite error – of not realizing that you can waste your vote if the election is FPTP – has likewise declined in other realms.

    As to (b), I recall seeing a letter to the New Statesman just before the 1992 election where a Labour supporter declared he was voting Lib Dem in his constituency this time, just to get the Tories out; noting that he had hung a banner from his house announcing that he was doing this; and asking (rather plaintively) whether Lib Dem supporters in other constituencies, where Labour was stronger, might consider returning the favour. Fast-forward to USA 2000 and you have the “Nader Traders” arranging vote swaps on the Internet. If the main objection many people have to tactical voting is losing the chance to give expressive support to their own preferred party, then vote swaps remove this objection.

    Ironically, the fact that US presidential elections take place in 51 constituencies (and require an absolute majority of the successful candidates to elect a President right away) makes vote swaps (or the threat thereof) much more potent than if the Presidency was a simple nationwide FPTP race.

  10. “Ironically, the fact that US presidential elections take place in 51 constituencies ”

    This has another impact which I don’t think many people have absorbed.

    In the state I live in, the last time a Democratic presidential candidate got less than 58% of the vote was in 1992. If I prefer the Democrats to the Republicans, and choose to throw away my vote on some minor party candidate, if this one vote actually costs the Democrat the state it would probably mean he would lose in a 48 state landslide instead of a 47 state landslide. It essentially takes a nationwide landslide for the Republicans to carry the state. So its pointless for me to vote tactically (and arguably to vote at all, this is one reason FPTP depresses turnout).

    Alot of the “blame Nader for the 2000 result” argument overlooks the fact that votes for Nader had no consequence of any sort in 48 states and the District of Columbia, which were either won by Bush with a majority, or carried by Gore. Though of course even if you just look at the nationwide vote totals, Gore won a plurality anyway.

  11. Many people vote for a party because they hope that party will win – the best way to predict a result is not asking “how will you vote” but asking “who do you think will win”. When two big parties alternate in power, their voters simply hope their party will govern this time by winning a seat-majority.

    But then the question is: why do so many people vote for Lib-Dem allt those years? Surely few think Lib-Dem could ‘win’ in the sense of forming a government on its own. Why haven’t they been persuaded by the ‘psychological effect’ to abandon the third party? Did they just want to confirm their existence (“a third option is still surviving”)? Or did they always hoped for a situation where they are the kingmaker between the big two? (Do they hope to stay in that position with elections by PR?)

    In that case, they must have mixed feelings after this election: both coalition options weren’t equally possible (mathemathically): a Lib-Lab coalition didn’t have a majority.

  12. Pingback: The Electoral Reform Society blog

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