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problem last June, in response to an inquiry by the U.S. Securities and Exchange Commission. At that time, the company said that 8.7 percent, or 83 million, of its 855 million active accounts were duplicates or false or "undesirable" for activities like the spreading of spam.

Mr. Sullivan said that since August, the company had established a new automated system to purge fake "likes." The company said it had 150 to 300 staff members to weed out fraud.

Flags are raised if an account sends out hundreds of friend requests at a time, Mr. Sullivan explained, or likes hundreds of pages simultaneously or, most obvious of all, posts a link to a site that is known to contain a virus. Those suspected of fraud are warned. Depending on what they do on the site, accounts can be suspended.

In October, Facebook announced new partnerships with anti-virus companies. People on Facebook can now download free or paid anti- virus coverage to guard against malware.

"It's something we have been pretty effective at all along," Mr. Sullivan said.

Facebook's new aggressiveness toward fake "likes" became noticeable in September, when brand pages started seeing their fan numbers dip noticeably. Brand pages were expected to lose, on average, less than 1 percent of fans, Facebook said at the time. But the thriving market for fakery makes it hard to keep up with the problem. Gaston Memorial, for instance, first detected a fake page in its name in August; three days later, it vanished. The fake page popped up again Oct. 4 and this time filled up quickly with the criticisms of the Obama administration.

Dallas P. Wilborn, the hospital's public relations manager, said her office had tried to leave a voice mail message for Facebook but had been disconnected; an e-mail response from the social network said that the fake page did not violate its terms of service. The hospital submitted more evidence, saying that the impostor was using the company's logo.

Eleven days later, the hospital said, Facebook found in its favor. But by then, the local newspaper, The Gaston Gazette, had written about the matter and the fake page had disappeared.

Facebook declined to comment on the matter and pointed to its Statement of Rights and Responsibilities.

The recent U.S. election season provided many accusations of fakery.

In Washington State, two groups fighting over a referendum on gay marriage locked horns over "likes" on Facebook. A group supporting gay marriage pointed to the Facebook page of its rival, Preserve Marriage Washington, which collected thousands of "likes" in a few short spurts. During those peaks, the pro-gay marriage group said, the preponderance of the "likes" came from far-flung cities like Bangkok and Vilnius, Lithuania, whose residents would seem to have little reason to care about a state referendum in Washington. The "likes" then fell as suddenly as they had risen.

Accusations were leveled on the Web site of the gay marriage support group, Washington United for Marriage. Preserve Marriage Washington denied any wrongdoing. Facebook declined to comment.

The research firm Gartner estimates that fewer than 4 percent of all social media interactions are false today but that the figure could exceed 10 percent by 2014.

Fake accounts and their fake posts will have to be culled aggressively if Facebook wants to expand its search function, said Shuman Ghosemajumder, a former Google engineer whose start-up, Shape Security, focuses on automated fakery on the Internet. If you are doing research on laptop computers, for instance, Facebook will have to ensure that you can trust the search results that come up.

"If the whole idea behind social search is to look behind what different Facebook users are doing, then you have to make sure you don't have fake accounts to influence that," he said.

The ubiquity of Facebook, some people say, compels them to be a little bit fake. Colleen Callahan, who is 25, is among them. She was a senior in college when she started getting slightly nervous about the pictures that a prospective employer might find on Facebook. Like the pages of most of her college friends, she said, hers had a preponderance of pictures from parties.

"It would be O.K. if people saw it, but I didn't want people to interpret it differently," she said. So Ms. Callahan tweaked her profile. She became Colleen Skisalot. ("I am a big skier," she explained.)

The name stuck. She still has not changed it back, though she is no longer afraid of what prospective employers might think. She has a job -- with an advertising agency in Boston, some of whose clients advertise on Facebook.