Undecided voters watch John Kerry and George W. Bush debate in 2004. (Richard Morin / The Washington Post)

It's no secret that only a small fraction of the population really remains undecided over the course of the campaign. Now two political scientists, UCLA's Lynn Vavreck and George Washington University's John Sides, have estimated just how small that fraction is: 6 percent.

Vavreck and Sides, along with collaborators Simon Jackman and Michael Tesler, had YouGov conduct a poll of almost 44,000 people in December 2011, asking who they would support in a Romney-Obama match-up. 94 percent of respondents said that they had made up their minds, and only six percent were undecided.

The team then interviewed the same 1,000 people out of that sample every week from then to the present. They found that the results have remained remarkably stable. Of those who originally said they'd vote for Obama, 2 percent have switched to Romney and 2 percent have become undecided. Of those who originally said they'd vote for Romney, 3 percent switched to Obama and 3 percent switched to undecided.

So the "undecided" count has stayed pretty constant at 6 percent. It's just a different group of people each week.

What about the people who were undecided in December? Who are they breaking toward as the race heats up? 30 percent are still undecided, but 70 percent now state a preference. Of those, 37 percent back Obama and 33 percent back Romney, and, more recently, Obama's support among these undecideds has been on an uptick:

Source: Lynn Vavreck

What accounts for this, however, is party identification. In the poll, undecideds were split roughly a third between Democrats, Republicans and independents. The previously undecided Democrats and Republicans, unsurprisingly, are breaking toward their parties' nominees. But 55 percent of independents are also breaking toward Obama, with 62 percent of independents having made their minds up since July of this year. Obama is gaining a disproportionate number of women, suggesting that Democrats' "war on women" rhetoric is resonating.

Who are these undecided voters? Mostly, Vavreck writes, casual observers of politics. "They are less interested in politics than voters who have made up their minds; they know less about politics; they are more likely to be moderates or unaware of their political ideology; and they are less likely to have a party identification," she explains. Only 40 percent of undecideds knew John Boehner is a member of the House, compared with 64 percent of decided voters.

But think about what a tiny fraction of the population this is. Undecided in December 2011 are six percent of voters. A third of those are independents. And Obama is winning that demographic by 4 percent. So Obama's edge among undecided independents comes down to the support of 0.08 percent of voters. That's one out of every 1,250. It's a reminder of how stable the race has been for most people, and how dependent the outcome is on the decisions of a small handful who aren't particularly interested in politics.