Polls: How big a bounce did Mitt Romney get from the debate?

Forget the conventional wisdom that debates don't really make a difference. Last Wednesday's seems to have been a game-changer for Mitt Romney.

At least, that's what the latest poll from the Pew Research Center would have us believe.

The respected poll, which came out Monday, was the best news yet for Mr. Romney. For starters, it now puts him ahead of President Obama by four percentage points among likely voters (49 to 45 percent). In the last Pew poll, taken three weeks earlier, Mr. Obama led among likely voters by eight points.

That's a big shift. And unlike many of the seven-day-average tracking polls that have been published in recent days, all the polling was done in the days after the debate (which respondents also said, about 3 to 1, that Romney won).

The poll contained other good news for Romney. His favorability rating grew five points since September and hit 50 percent for the first time since Pew began polling voters on the question. Obama's favorability rating fell from 55 percent to 49 percent.

Romney's supporters also appear to be more engaged. A full 82 percent say they have given a lot of thought to the election – a sharp rise from September, and considerably more than Obama's supporters, of whom 67 percent say they have given a lot of thought to the election.

In addition, Romney gained ground in nearly every specific category that Pew polled on, including how voters view him as a leader, how willing he is to work with leaders of the other party, and how well he connects with ordinary Americans.

So what's the catch?

For one, some people have criticized the Pew poll for a more heavy makeup of Republican voters. In Pew's September poll, 39 percent of likely voters considered themselves Democrats, compared with 29 percent who considered themselves Republicans. In this latest October poll, that flipped, with 31 percent of likely voters considering themselves Democrats and 36 percent considering themselves Republicans.

The poll's defenders say that the shift is simply a function of voter identification being fluid: After the debate, more people might have decided to call themselves Republican, or more of those Republicans might have been likely to vote. Not adjusting for that helps capture an important dynamic in a shifting electorate.

The timing of the poll – it was conducted in the three days immediately after the debate, with most of the interviews taking place in the first part of that period – also more heavily accounts for any bounce, however short-lived, that Romney might have gotten from the debate. But this doesn't necessarily give a good idea of the longer-term trends or whether that bounce will last.

Also, while respected, Pew is just one of many polls – and some of the other polls released Monday were less favorable to Romney.

Gallup's latest tracking poll, which averages seven days of data, still put Obama five points ahead of Romney among registered voters (a distinct category from "likely" voters; among registered voters, Pew had the two candidates tied). For the three days immediately following the debate, Gallup also showed the candidates tied among registered voters.

Both the Gallup and Rasmussen tracking polls that came out Monday actually showed a slight improvement for Obama from the day before. And they seemed to indicate that Romney's bounce – while real – was fading a bit, perhaps in reaction to Friday's unexpectedly positive jobs report or perhaps as enthusiasm for the debate settled into the background for voters.

The conflicting polls can be understandably confusing for election-watchers: Which to believe? Which pollsters do it best? Should you look at "registered voter" or "likely voter" numbers? Should polls adjust for party identification?

They reflect the fact that polling is, at best, an imperfect science with a lot of disagreement about how to do it right. At this point, the polls also probably reflect voters who are still making up their minds about how they feel about the two candidates and whether the debate really changed their opinion.

At The New York Times's FiveThirtyEight blog, pollster Nate Silver gives a fair amount of validity to the Pew poll – which was significant enough that, by itself, it managed to shift the chances of Romney winning the electoral vote in his model's forecast from 21.6 percent to 25.2 percent. But, he also notes, common sense and a look at the fundamentals of the race right now don't really point to a four-point advantage for Romney.

"The evidence that Mr. Romney’s bounce is receding some is only modestly strong – as opposed to the evidence that he got a significant bounce in the first place, which is very strong," Mr. Silver writes. "Still, the order in which polls are published does not exactly match the order in which they were actually conducted – and at turning points in the race, these details can make a difference."

So whom to believe? At this point, voters may need to wait a few more days to see how the polling settles out – or until the next debate, when there could be yet another bounce for one of the candidates.

The vice-presidential debate is Thursday; the next presidential debate – town-hall style – is Oct. 16. Stay tuned.