There aren’t many certainties around the UK General Election due in May, so everyone says. As the proportion of voters backing Labour or the Tories, even under First Past The Post, dwindles, the maths become much more unpredictable. Sure, it seems extremely likely that the SNP will be the third largest party, eclipsing the Lib Dems, but that seems so plausible partly because so few people have any idea why anyone would still vote Lib Dem. But some continue to do so, inexplicable as it is.

Screen Shot 2014-12-30 at 12.49.10One thing that seems almost certain, though, is that there will be no Tory/UKIP coalition, barring a ‘kipper surge from the ~15% they’re currently polling.

The numbers and mechanics of majorities are vertiginously stacked against it. To the left are the five constituencies where the bookies think they’re going to win (h/t Kris Keane): Carswell’s Clacton plus four more that do not include Mark Reckless in Rochester and Strood.

It seems like a plausible list, although tactical voting in both directions will make it pretty unpredictable.

Let’s start with two clear rules. No sensible smaller party goes into formal coalition where the larger party already has a majority (and few larger parties offer it). And no sensible smaller party takes part in a coalition where they don’t get their larger partners over the line.

So, assuming UKIP win just those five seats, the Tories would need to be between one and nine seats short of a majority for it to be even worth considering for either party (ten short plus UKIP would see it come down to the Speaker’s casting vote). But for the Tory party, being short by just one seat would be pretty indistinguishable from being ahead by just one. The DUP would probably vote for Cameron for PM, in the “one short” scenario, and even in the “one ahead” scenario they’d be vulnerable to every single Tory backbencher with a grievance or a principle. Why give Farage a bigger national stage to swap one sort of uncertainty for another?

No, in order for UKIP to be a plausible partner for the Tories, the latter would need to have fallen significantly short, yet the two together would have to comprise a clear working majority. For example (and this feels like the bare minimum for it to be considered), if the Tories were fifteen short and UKIP won twenty seats, then coalition might be possible. Just possible. UKIP winning twenty seats is a stretch to say the least (remember when Farage got beaten by a man in a dolphin costume when Labour and the Tories weren’t standing?), and the Tories being just the right amount short is also exceptionally unlikely (they were twenty short in 2010, although none of this takes into account the Sinn Fein MPs who don’t take their seats). Combine that with the natural antipathy between two parties from the same “family”, and the whole thing becomes vanishingly unlikely.

This scenario is written about as plausible, but only because it suits various people to do so (UKIP, the sensation-hungry in the media, Labour, the SNP etc). I’d say it’s about as likely as tossing two coins and having them both land on their edge. Just this side of impossible.