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Confusion over British elections and the relevance to political punditry of a dictum of Bill James

I’m no expert on British politics, so maybe I’m actually the confused one. Anyway . . .

John Lanchester writes in the London Review of Books:

Labour have an enormous statistical advantage going into the election. The simple way of putting this is to say that votes in the country are worth less than votes in the city. That’s because the Boundary Commission has struggled to keep up with the historic drift of Britons out of cities into the country . . . Country constituencies are bigger, in population as well as geographical terms, than urban ones . . . Because Labour’s support skews urban and the Conservatives’ skews rural, this translates into a big advantage for Labour. How big? Well, this non-partisan article from the House of Commons magazine, dating from 2006 when the election was a long way off, reckoned that the Tories needed to win the election by a margin of 10 per cent in order to have any majority at all.

If you follow the link, though, it appears that (a) the boundaries were redrawn in 2005 or 2006, so the boundaries are only 4 or 5 years out of date, and (b) the “10 percent majority” thing is not coming from any imbalances in district sizes:

The Conservatives will still need a swing of about 10 per cent to win power outright . . . A swing of just over one per cent will now cost Labour its overall majority, compared to 1.8 per cent with boundaries unchanged. The changes reduce the swing needed by David Cameron to secure an overall majority from 11 per cent under the old boundaries to nine or 10 per cent with the constituencies which will be used in the next general election . . .

Got that? The effect of redrawing the district lines is estimated to be something like 0.7% of the vote, not 10%. (I’m getting 0.7% by subtracting “just over one per cent” from “1.8 per cent.”) If the boundary change in 2005 or 2006 comes to the equivalent of 0.7% of the vote, then I’d expect any population shifts since then to account for less than 0.7% in partisan advantage.

Less than 0.7%. Not 10%.

The 10% is coming from the multiparty system, which has at times benefited the Labour party and at times benefited the Conservatives and doesn’t seem to have benefited the Liberal Democrats at all (yet).

Bill James has a dictum that the alternative to doing good statistics is not no statistics but bad statistics. People who choose not to take numbers seriously–that is, as numbers–do not simply ignore numbers; rather, they treat them as words. In baseball, that meant, for example, going gaga over free-swingers who hit .300 in a hitter’s park and underrating low-average power hitters who draw walks. (Or, at least, that’s how things used to be before James and others popularized on-base percentage, slugging average, and all the rest.)

In the political context, Lanchester is pulling out numbers without regard to their magnitude–1%, 10%, what’s the difference? He wants to understand the political system–I respect that–but he doesn’t know where to start, so he picks out numbers where he can. I don’t think he’s trying to mislead, I just think this is what happens when you take numbers as words.

P.S. I happened to notice this one because I followed the link from Helen DeWitt’s blog. More generally, though, I notice a fair amount of innumeracy in the London Review of Books and (back when I used to subscribe to it) the New York Review of Books. For example, here, here, here, and here (from Gary Wills, Frederick Crews, David Runciman, and Samantha Power).

These people are all busy writers, and I can hardly expect them to find the time to think quantitatively, so I think a statistical copy editor would be a good idea. I think they could hire Ubs to do this for a reasonable fee, for example.

P.P.S. Yes, I know, hitting .300 in the majors is no mean feat. There’s no way I could hit .003 in any park. You could put me at bat every day for the rest of my life against anybody–major league, minor league, whatever–and I’d never even come close to getting a hit. The point above, though, is about comparisons of world-class athletes, which we can attempt even if we are leagues and leagues below them in ability.


  1. dWj says:

    I believe that British constituency boundaries tend to be drawn using much older population data than are used in the US, where we do a detailed census followed fairly promptly by redistricting. In the US, districts are "out of date" by approximately their age, while in Britain they are typically somewhat more out of date than that.

    It seems to me the total effect should not be counted as 10%, but as 5% or 6% or somewhere thereabouts; for Labor and the Conservatives to end up with the same number of seats, the Tories don't need an extra 10 percentage points of the vote; that's to get to half of the Commons.

    Your main point, though, that the problem isn't mostly one of being out of date, is correct.

  2. Tom Brunell says:

    The anti-Tory bias in the UK Is huge, especially by American standards. Ron Johnston (and his colleagues) have a new paper out with new estimates for bias in the UK for 3 parties and, off the top of my head, the bias costs the Conservatives between 30 and 50 seats!

  3. Jeremy MIles says:

    Here's a link to a discussion of an old paper of Johnston's (I couldn't find the new one – although I didn't look beyond Johnston's departmental homepage).

    British elections are more complex, because there are 3 way races, and tactical voting. E.g. in the last election, some people in safe labour seats voted lib-dem as a protest against the Iraq war. However, in a closer election (like this one) those same people might not want to risk a conservative victory and will vote Labor. There was a website set up called (something like) which advised a person whether they would be safe making a protest vote in their constituency or whether they should continue to vote labor. I don't know how popular it was, but I know people who used that strategy.

    The Guardian newspaper has a 3 way swingometer –… although they assume a consistent shift, which is scuppered by tactical voting.

    That said, I've heard a lot less about tactical voting in this election – maybe that's a sign that people are not as worried about a conservative victory as they were?

  4. Phil says:

    Lanchester seems to have translated "a swing of about 10 per cent to win power outright" into "win the election by a margin of 10 per cent in order to have any majority at all".

    There are two problems here. Firstly, the swing is a measure of the change from vote 1 to vote 2, and has nothing to do with the margin in vote 2. If the Labour/Tory vote share went from 41:59 to 51:49 that would be a 10% swing, giving Labour a 1% margin.

    Secondly, votes aren't seats: in a multi-party system, the winning party will always have a sizeable margin in votes over the runner-up, because the definition of winning is gaining an absolute majority of seats. The party that wins the largest single share of the popular vote hasn't necessarily won the election at all. There may be a difference in the size of the margin Labour and the Tories need in order to win a majority of seats, but it's not a huge one – the Electoral Commission sits regularly enough, and has broad enough membership, to keep huge disparities from developing. The Tories may need a large swing in order to get a given margin, but that's an artifact of comparison with the previous election.

  5. Helen DeWitt says:

    Well, I'm now embarrassed to have linked uncritically, argh. Drive-by linking, argh.

  6. zbicyclist says:

    Tim Harford had this story on "More or Less" (BBC4, podcast), basically supporting the notion of large bias.

    I'd be inclined to give Harford the benefit of the doubt on British statistical issues.

    It's on this show:

    While looking for the specific show reference, I came across this quote from Winston Churchill — of no use to the present discussion, but worth remembering anyway:

    Winston Churchill once said: "When I call for statistics about the rate of infant mortality, what I want is proof that fewer babies died when I was Prime Minister than when anyone else was Prime Minister."

  7. Andrew Gelman says:


    I believe the experts who say that, given current voting patterns, the U.K. system is biased against the Conservatives. What I don't believe is that much of this bias is coming from differences in constituency sizes, which is what Lanchester was saying.

  8. Steve Sailer says:

    Malcolm Gladwell would be a good example of a verbalist who could benefit from hiring a statistical editor. It's not considered shameful for somebody who is good with numbers (e.g., Steven Levitt) to work with somebody who is good with words (e.g., Stephen Dubner), and rightfully so. Everybody benefits.

    Therefore, it should be routine for talented nonfiction writers to get help from somebody more quantitative, just as successful Wall Street firms tend to be a combination of salesmen and quants.

  9. Ed says:

    British electoral law does allow for a much bigger difference in population between constituencies than in the US (as does Canadian electral law as well). Since the largest population constituency, the Isle of Wight, has a population of 130,000 and US Congressional districts now average about 720,000 given the most recent estimates, in absolute terms the effect of this is fairly muted.

    Scotland until recently had smaller population constituencies than England, and since the Tories were relatively weak in Scotland this effectively cost them several seats. However, this imbalance has been corrected, and at any rate I've seen no arguments that urban constituencies within England had smaller populations than rural constituencies. Within England, a system of constituencies with relatively equal populations was instituted in 1885, with a number of anomalies that were removed by 1949.

    What has happened is that the Tory vote in most urban constituencies collapsed in the 1980s and 1990s, followed by very low turnouts (people are less inclined to vote in places effectively contested by only one party). So Labour wins large number of seats on low totals of absolute votes, in a number of urban seats where they effectively have no competition.

    As it happens, something of the same thing happens in the US, where the Democrats win a number of urban congressional districts with high immigrant populations, on relatively low vote totals. However, this is cancelled by other imbalances which favor the Republicans, and also we are dealing with a situation where there is low turnout in these seats because large numbers of the people "represented" there can't vote because they are not citizens. So this is both a more and a less serious problem than in the UK.

    Absent gerrymandering, anomalies like this happen but tend to even out over time. The boundaries, again drawn by a neutral commission, tended to favor the Tories over Labour in the 1940s and 1950s.

  10. Tom Rees says:

    Right-wing parties have an advantage over left-wing ones in first-past-the-post (rather than proportional representation) systems… but that's another issue!