The TV pundits disagreed, so did focus group members, the polls and , of course, the campaigns.

So who won the debate?

At least some people closely watching the contest — those betting money on the election’s outcome — did offer a kind of consensus view: President Obama soundly beat expectations in his second contest against Republican challenger Mitt Romney.

During the course of the night, at three sites where participants essentially bet on who will win, shifts in wagering reflected the fact that the perceived odds in favor of Obama winning the election were rising.

The votes on well-known political betting site reflected a jump in the president’s chances from 61.7 percent just before the debate to 64.1 percent shortly afterward.

Putting a value to the candidate's chances (The Washington Post/Source: Intrade The Prediction Market)

Similar jumps could be seen in other markets, too. At the betting site, the president’s chances jumped 2.7 percentage points during that period, and on the Iowa Electronic Markets, run out of the University of Iowa, his chances were up about 2.4 percentage points in that time frame.

“Traders saw something in the debate that raised [the president’s] price,” said University of Iowa professor Joyce Berg, who is also the director of the Iowa Electronic Markets.

Exactly how to determine who has won a debate or is winning an election contest, of course, is a tricky matter.

Polls are often close but fallible for a variety of reasons, including whether the sampled voters accurately reflects who will actually vote.

Shortly after the debate, CNN announced that its polling of 457 registered voters who watched the debate showed that 46 percent thought Obama won the debate and 39 percent thought Romney won. But that poll had a plus-minus margin of error of 4.5 percentage points. And in contrast to the headline numbers, most thought Romney would do a better job handling key issues such as the economy and taxes.

Given the complications of polling, some political watchers have shown interest in the betting sites that allow participants to wager on the election’s outcome. The prices for laying a bet reflect the perceived odds at the time for any given candidate.

Unlike polls, which reflect what a group of voters is thinking at a given moment, these betting sites, or so-called “prediction markets,” offer another method for drawing on the “wisdom of crowds.” Moreover, because participants have money riding on their guess, they may be more inclined to reflect more on the issue than the average person answering a pollster.

“Our traders are trading with their heads, not their hearts,” Berg said.

As many have noted, the bettors, unlike TV pundits, are less likely to let their own political beliefs alter their judgement because money is at stake.

“What’s useful is that it has a sense of perspective that commentators don’t,” said Justin Wolfers, an economist at the University of Pennsylvania’s Wharton School.

On the other hand, there is the possibility, particularly as more people look to such sites for reflections of the zeitgeist, that some deep-pocketed campaigns could make bets to manipulate the perceived odds.

“The strongest argument for predictions markets is that all the alternatives are so dreadful,” said Wolfers.