For all of you privacy fundamentalists, Facebook has a new, friendly, sympathetic face: It will let you log into applications anonymously by clicking on a highly visible button. So third-party developers will not collect any information about you, and those pesky apps won’t post on your wall.

“Great optics," Chris Taylor says on Mashable. He’s right: Here’s Mark Zuckerberg, whose monetization strategy for Facebook depends on the willingness of users to share information with his company, offering people a chance not to share it. Except that the personal data of Facebook users are being withheld from outside developers, not from Facebook itself, so Zuckerberg is being generous at the expense of others.

There is one other reason that the social network’s newfound respect for privacy is less than it seems. Facebook knows, and has known for years, that the number of fake accounts has been growing with its user base or faster, that bots run rife, and that there is no way to check the information that more than 1 billion users provide in their profiles. The promise of ad targeting that Facebook makes to advertisers is already suspect, and that won’t change significantly with an anonymity button.

In March 2012, Facebook said 5% to 6% of its 845 million accounts were false or duplicate. In its 2013 annual report, however, it put the number of duplicates—accounts maintained by people in addition to their primary ones—between 4.3% and 7.9%. Add to that 0.8% to 2.1% of “user-misclassified" accounts, such as ones created for cats and dogs, and 0.4% to 1.2% of “undesirable" accounts, such as those meant specifically for spamming, and the total share of fakes is in the range of 5.5% to 11.2%.

In the best-case scenario, that means Facebook is now aware of almost 68 million fake accounts. Yet the range of the estimates is so wide that the company clearly has no idea of how much of its 1.3 billion user base is fluff.

In 2012, Facebook unleashed a highly publicized war on fakes, using algorithms to weed out dummy accounts from the fan bases of stars like Rihanna and Shakira.

I know, however, that the effort is rather futile. I have more than 97,000 subscribers on Facebook, and most of these either appear fake according to Facebook’s own checklist, or come from countries where people don’t speak my language. I post mainly in Russian, but thousands of my so-called friends only use Arabic or Hindu on their walls. I don’t know anyone named ???? ???????? from Saudi Arabia, but he or she apparently follows what I write, while only ever posting in his or her native language. People such as ???? ??????? are often first to “like" my posts. These likes look ridiculous and create the impression that I went to one of the numerous sites where Facebook subscribers are bought and sold, to purchase a mixed bag of so-called fans to bolster my popularity. (No, I didn’t, in case you were wondering.)

The fake subscribers appeared in droves after I started posting about the 2011-2012 protests against the rigging of the Russian parliamentary election. Many of those who reported from the Moscow rallies noted a similar influx. In 2014, the fakes are still there. I can’t take the time to report each of them to Facebook for removal, because there are thousands.

I can only imagine how many non-existent fans Rihanna must still have.

To this day, I have no idea why the fakes came. I suspect, however, that they are part of a social botnet like the one that researchers from the University of British Columbia created and ran on Facebook in 2011. Their bots were so good they even got friend requests. Such networks could be used to steal information from legitimate accounts or secretly promote products or ideas. Facebook may fight them, but it took me all of 10 minutes to locate and contact a botnet operator today.

In 2012, the BBC asked a Facebook spokesman about the dummy accounts. “We don’t see evidence of a ’wave of likes’ coming from fake users," he replied. “With regard to the geographic origin of fans; interest in products tends to spread organically through friends and friends of friends. Often these connections will be international." The spokesman also said the company did not “see evidence of a significant problem" with ad targeting.

It is, however, a problem that the social network doesn’t know whether 5% or 11% of its user base (or could it be more?) doesn’t exist. And the targeting is probably a little bit off, if the ads I now see on my wall are for women’s clothing and a drawing course, though I lost interest in practicing the visual arts in the early 1980s. The advertisers must have messed up the targeting, but Facebook doesn’t really know who I am, anyway. In deciding which ads to show, it faithfully uses information provided by account owners, and a couple of years ago, I said on my profile that I work for the global government as a minister without portfolio. My friends liked the joke, so I left it there. Facebook has asked me to provide information about my employer’s location—it has algorithms that check the provided information against some database—but I have been hesitant to respond: I don’t really know where the global government might be located.

I am not saying that ads on Facebook don’t work—judging by the company’s rapid revenue growth, it has a lot of satisfied customers. The matter under discussion is privacy. Although anonymous and misattributed accounts, as well as bots, violate Facebook’s data use policy, lots of people—who knows how many—create and use them anyway, because the social network is unable to police its huge user base effectively.

That has always made true privacy, even total anonymity, available on Facebook to all takers. Much of the all-important personal information on the network is garbage, and a button that allows people to conceal it from an app is a pretty gesture. Thanks, Mr. Zuckerberg, but it’s not much use. Bloomberg