Unfortunately, neither of the approaches you suggest will be effective. Your only viable avenues for relief would be to legally pursue the persons/entities who libeled your business, assuming they did in fact commit defamation, you know who they are and the reviews are causing you sufficient harm to warrant the often substantial expense of civil litigation. If you don't know who they are, it might be possible to force Yelp to identify them, however you will not be able to hold Yelp liable or force Yelp to remove the reviews or delete your company name from their listings. The only way to compel removal of a defamatory post is by way of a petition for injunctive relief in a court of competent jurisdiction.
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I disagree with Mr. Adli's response.
There is, of course, no possibility that Yelp or similar sites will let you simply opt out of the public discourse about your business. But Yelp and similar sites have adopted very specific and explicit "Content Guidelines." If the CG's are violated by any review of your business, you have only to make your case persuasively and the site administrators will remove it. I have accomplished this for any number of CA licensed professionals and businesses (I accept ONLY State licensed businesses and professional services providers for this legal service) so I am speaking from first-hand experience here.
I can tell you without reservation that the evaluation of any review by the site against the CG's is objective, fair, impartial and consistent. The site is deeply invested in the efficacy and integrity of the CG's -- and only that. It is not invested in your business, nor in having as many reviews as possible, or any other secondary consequences. The CG's are the value to be protected by site administrators and their focus is singular.
The site is completely unresponsive to any threats or demands about defamation. The site does not care if some of the reviews of your business are wrong. The site believes that the erroneous reviews and posts will be outweighed by the consistency and quantity of the other reviews. The site is not invested in vouching for the accuracy or legitimacy of every review, but only in providing a process where the numbers will tell the tale.
If you have evidence that a fake review is planted by a competitor, present your evidence to site administrators. You will get a clinically fair if ruthless evaluation of your claim. Of course, there has to be evidence -- not just your hunch or suspicions.
Of course you can sue any reviewer, but be prepared for a lot of unexpected consequences. California has a robust anti-SLAPP statutory scheme and, if your claim is not sound, you are likely to wind up with a court order requiring that you pay the other party's considerable legal fees as well as your own. It can take more than a year just to resolve the anti-SLAPP issues -- a very expensive and very long year plus. In the meantime, the disputed review stays up on the site.
Remember that opinions -- even wrong ones; even opinions that are not clearly identified as opinion -- are not actionable as defamation.
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I do not see Ms. McCall’s approach as viable since it does not sound like you have evidence that would prompt Avvo to take down any reviews. As you indicated, at this point you only “suspect” or feel that “there is a chance” that one or more reviews might be fake or submitted by competitors. Accordingly, I would second my colleague Mr. Adli’s response and suggested approach.