Walk into the “filing center” at a presidential debate and you’ll see hundreds of reporters seated at tables doing two things: Watching the action on TV (reporters covering the debates aren’t actually in the same room as the candidates) and monitoring Twitter on their laptops.

They are hard at work on one of the most elaborate exercises ever undertaken in groupthink.

This was to have been the campaign when Twitter and other social media allowed new voices to enter the debate, delivering a more diverse array of opinion and helping candidates reach beyond the media filter. In reality, social media have had the opposite effect, causing conventional wisdom to be set, simplified and amplified, faster and more pervasively — and nowhere is that more evident than in the debate coverage.

From the first minutes, journalists at the site and back at home monitor each other’s tweets, testing out themes and gauging which candidate is ahead, point by point: “First section kind of a wash. . .Romney very soft on Libya. . .Obama is condescending here . . .Zing!. . .No laughs in the press file for that canned Obama line.” Somewhere around the 30-minute mark, the conventional wisdom gels — and subsequent tweets, except those from the most hardened partisans, increasingly reflect the Twitter-forged consensus. Well before the end, the journalists agree on a winner, a loser and which moments — Big Bird, binders full of women, horses and bayonets — should trend their way into the news coverage.

“First 30 minutes: Obama better than Romney,” my friend Chris Cillizza, who runs The Post’s blog The Fix, tweeted at 9:32 p.m. Monday. Ben Smith, the highly regarded head of BuzzFeed, retweeted Cillizza’s tweet that same minute.

At 9:37 p.m., The Post’s Karen Tumulty shared the news that conservatives on Twitter think “Romney has been surprisingly timid.”

“Obama is doing what he should have done in the 1st debate,” the Huffington Post’s Sam Stein postulated at the same time.

By 9:45, National Journal’s Ron Fournier concurred that “Obama seems to be winning on points.” At 10:08, the Daily Beast’s Andrew Sullivan cemented the CW with his view that “Obama is wiping the floor with him.”

Four minutes later, an exultant David Corn of liberal Mother Jones asked whether Romney had “landed a single blow on Obama.” A few minutes after that, even the editor of the conservative National Review, Rich Lowry, was giving in to the CW, saying he had thought Romney “shld try to be a little above the fray, but this is a bit much.”

I don’t fault the journalists who engage in instant analysis; the ones I named are among the best in the business. I use Twitter myself to monitor the congealing wisdom. But our political dialogue may lose something because of this pre-publication and pre-broadcast collusion. In this case, social media is discouraging people from challenging the CW.

Not too long ago, the wire services, broadcast networks and newspapers covered major political events differently. Each outlet had its own take and tidbits. But now everybody is operating off the same script and, except for a few ideological outliers, the product is homogenous.

In the first minutes of Monday’s debate, journalists on Twitter launched various pet theories. “Romney going to left of Obama sort of so far?” NBC’s Chuck Todd inquired at 9:09.

Conservative Hugh Hewitt saw hopeful signs for Romney at 9:13, alternating the Republican candidate’s own words with the word “boom.”

The Atlantic’s Molly Ball thought she saw, at 9:14, “the Romney of the first debate vs. the Obama of the 2nd debate.”

But the view spread that Romney was too soft. “Obama is just brutalizing Romney here. I mean, HAMMERING him,” Cillizza opined at 9:12, then asked his tweeps: “Obama feistier tonight than in 2nd debate, right?”

About that time, Fox News’s Ed Henry joined the emerging Obama-is-ahead consensus. “Obama seems more comfortable weaving his way around world,” he tweeted at 9:17. “Romney appears to be watching every word carefully to avoid gaffe, v cautious.”

Around the halfway point, ­TheWeek.com’s Marc Ambinder helped to shape the view that “Romney thinks it’s better to be safe and lose this debate but cross a minimum credibility threshold.”

As the debate ended, National Journal’s Fournier judged Romney’s performance “far from exceptional,” and NBC’s Todd was labeling Romney’s strategy “a tad meek.”

At 10:32, The Post’s Cillizza read out the final verdict. “Obama’s strongest debate. Romney’s weakest,” he tweeted. “But will it matter?”

A worthy question. But that meme will have to trend another day.