Why hung parliaments are now much likelier than before

This will be my only blog post on the forthcoming UK election.votelogo2

Although most people now know me as a political theorist, specialising on the 17th century philosopher Thomas Hobbes, I started my career as a quantitative political scientist, studying the decline of the British electoral system and how votes are turned into seats. Why did the Conservatives only have a 21-seat Commons majority in 1992 when they led Labour by 8 percentage points in votes, while Labour’s 9-point lead in 2001 gave them a 167-seat majority?

Unravelling the different factors here is incredibly complicated – far more so than you might think. I produced the only method which estimated these different components at the actual election result; everyone else computed them under hypothetical conditions, sometimes implausible ones. For more details, see my 2004 article in the journal Electoral Studies, or for a simpler version, pp. 234-7 of my 2008 chapter in Robert Hazell, ed., Constitutional Futures Revisited (Palgrave Macmillan).

One key contribution was to show, for the first time, that the key influence on hung parliaments was the number of minor-party seats. This might seem obvious, but at the time, the dominant explanation was the decline of the so-called ‘cube law’: first-past-the-post should magnify a small lead in votes into a larger lead in seats, but the amount of magnification had shrunk over time. I showed, however, that this effect was trivial compared to the impact of minor-party seats. My equation was:


which has an intuitive explanation: if minor parties win no seats, a fairly small lead in votes will be magnified into a secure majority, but the more seats minor parties win, the larger a party’s lead must be to get a secure majority, which thus becomes harder and harder. I needed to make a lot of simplifying assumptions to get this far, but the very rough estimate was that there is approximately a one-in-four chance of a hung parliament, and a one-in-three chance of a government with a majority of under 25 seats.

Again, I was the first person to make this calculation directly rather than (for example) making inferences about what past results might hold for the future. One journalist recently Tweeted about the unlikelihood of hung parliaments, based on election results since 1945. But in the early post-war period, minor parties won almost no seats. It’s a different world now.

OK, enough of modernity: back to Hobbes.