Stephan Shakespeare: Voters are now slightly more likely to vote for Cameron's re-election but they won't vote to leave the EU

Stephan Shakespeare is Chief Executive of YouGov. Follow Stephan on Twitter.

In a few hours, David Cameron will make a historic announcement that he will offer an in/out EU referendum after a period of negotiations for an improved relationship. It looks like a bold move, but it's also the safest bet: we want to feel in charge of our destiny, but we also want to stick together.

At YouGov we recently went back to our database and re-analysed some polling conducted between autumn 2009 and the 2010 election. It was one of those exciting moments you get from working with longitudinal data, when you can see how things really changed: of those who told us six months before the election that the were "absolutely certain" to vote for the party they then preferred, 20% had changed their voting intention by the start of the campaign. This accords well with the 'choice blindness' study I described last week which demonstrated that even strong opinions could be reversed in five minutes without the opinion-holder actually noticing.

So it should come as no surprise that the majority for an 'out' vote that we've been recording in our in/out EU referendum tracker should have suddenly collapsed (as my colleague Peter Kellner noted here from 51-30 to 34-40. That's a 27% swing in favour of EU membership in just eight weeks (from the end of November to last weekend). What happened?

For years, no-one of any note could be heard with a positive thing to say for the EU. Then David Cameron, Ed Miliband, Vince Cable, the American Embassy and Richard Branson all came out with something like European enthusiasm. Yes, they said, we need change but we need to stay. That's all it took, no actual change in iur circumstances. Just having authoritative figures reminding people of the arguments on the other side - especially, reminding people they have something to lose - can have a big effect. People's natural desire for continuity kicked in, or if you prefer it, their natural fear of change. Were there to be a real, decisive referendum campaign on the back of any tiny concession that could be dressed up as reform, the swing is likely to be much bigger. Barring some as yet unforeseen historic disaster, I find it hard to take seriously any other outcome five years from now.

Cameron's commitment to an in/out referendum therefore poses little risk to the Pro-Europeans; it is unlikely to lead to an 'out' vote, and that realisation will probably mean only minor concessions but no deep reform. Maybe that's ungenerous - maybe increased confidence in winning such a campaign would embolden the EU to embrace genuine change in the service of closer union. In any case, the real upside for Conservatives is that Cameron has just made it very slightly more likely that he will win a second term as Prime Minister.