The election result in the UK was astonishingly close the results predicted by the BBC/Sky exit poll, with the Conservatives at 307, somewhat short of a majority.

I don’t know what this means for arcane debates about uniform versus proportional swing; the swings during the night were all over the place. It’s possible that uniform national swing is still a better model than proportional swing, but the stochastic element looked huge. (And of course, it’s the stochastic element that the Curtice et al projection model models).

The Conservatives have now reached out to the Conservatives; former Prime Minister John Major has suggested that having `one or two’ LibDems in the cabinet would be a price worth paying to have stable government quickly.

I would suggest that’s a bad deal for the LibDems other things being equal (and bear in mind that the big other thing is electoral reform). One of the best supported law-like statements in political science — perhaps more law like than Duverger’s Law — is Gamson’s law.

Gamson’s law states that parties receive cabinet seats in proportion to their contribution to the seats in the majority.

At the moment, the Conservatives have 306/7 seats, the LibDems 57. That means that the LibDems have roughly 16% of the seats in a hypothetical Conservative-Liberal Democrat majority.

Now, the last Brown cabinet had 23 ministers. 16% of that is a little bit over three and a half. So a `proportionate’ share of ministers would be bigger than the number Major suggests.

UPDATE: More on this, together with normalized Banzhaf scores (woo!) at the LSE Election Experts blog.