There are many websites who let people anonymously attack studies just to disparage the authors. An example is Pubpeer (I confess that I had never heard of it before being warned by a colleague).
If I have my work attacked on a swindler website that protects the accuser's identity while exposing the author to embarrassment, what do I do?
Ignore it?
or
Get into an argument to prove that you are being deconstructed in a dishonest manner?
I know pubpeer only for being sued by a researcher who, it turns out, had to subsequently retract over 40 papers. So I wouldn’t call them a “swindler website” or probably the ACLU wouldn’t have gotten involved in defending them. If you get hit by a genuine crank, all you can do is ignore it - getting into an online argument is never a good idea. If it reaches genuinely defamatory levels, there is of course a court option. As these comments are left by anonymous users, I’d at least try to reach out to the site owners first.
It is probably a mistake to react in any way to cranks, no matter what they do. Consider that the Streisand Effect will just amplify their words.
Even a law suit is unlikely to be beneficial for the added reason that the people involved probably have too few assets to make it worth the effort, especially when you add in the additional publicity they get.
To some extent it depends on the website and the way they work. If at all possible there, I think I'd write a rebuttal in the most rational and unemotional style. I also think that scientific argument should not rely on the names of the people who argue. A criticism is not invalid or "swindle" just because the author is anonymous. Obviously there is unfair criticism and it may happen that somebody writes something "just to disparage the authors", but there are other reasons to remain anonymous, particularly the fear of having the own career sabotaged by influential people that can't take criticism. Criticism in my view is essential for science in order to improve, and all too often published results are taken as "true" by readers without checking the argument in any detail.
Ultimately in the eye of the impartial reader the style of the critic may or may not discredit itself, and if it doesn't, I'd say it is worth a proper reply. I appreciate people who react to criticism in an open-minded and reasonable way, and I'm surely not the only one. Obviously chances are it isn't worth the time to get engaged in a long debate, particularly if the criticism is based on lies and misrepresentations, however I would want to leave at least one reply making my point clear in a way that a neutral reader can see what my take on this is, and that I am willing to address issues in my work.
I'm not sure what other "anonymous websites" are you referring to, but PubPeer in particular is not something I would associate with a term like "swindler website". I would recommend everyone unfamiliar with PubPeer to take a look at their FAQ to judge for themselves whether their rules and procedures are rigorous enough for a legitimate post-publication discussion platform.
First and foremost, one of the key principles of PubPeer is that every comment needs to be factual and verifiable:
Q: What can my comment contain? Facts, logic and publicly verifiable information.
A: By far the most important rule for commenting is to base your statements on publicly verifiable information.
…
Allegations of misconduct are forbidden on PubPeer. They are anyway unnecessary. Your audience on the site is mostly composed of highly intelligent researchers and scientists. They are quite capable of drawing their own conclusions if the facts are clearly presented.
You should also avoid personal comments about authors and speculation about researcher actions and motives.
All comments on PubPeer are moderated to ensure they comply with the rules. You mention your work being "attacked", "disparaged" or "deconstructed in a dishonest manner"; does that mean the comments in question were in violation of these rules, or just that they perhaps exposed uncomfortable yet real weaknesses of the work?
Either way, the preferred course of action is to follow the FAQ again:
Q: My paper has been commented! What can I do?
A: PubPeer offers you a permanent right of reply. We encourage you to respond on the site. There are special facilities for indicating author responses. We believe that honest, careful and competent authors should provide “after sales service” for their publications, by clarifying any points that readers find unclear.
By engaging in the discussion, you can explain points of your work that were perhaps misunderstood by the commenter or inadequately supported by the data included directly in the paper.
Finally, note that whatever you publish would always get discussed both in public (at conferences or in journals) and in private (at various group and department meetings or Journal Clubs around the world). PubPeer just provides a convenient platform for such discussion that can work in the 21st century. The alternative of publishing thousands of articles like "Comment on Comment on Paper X" simply does not scale given current publication volumes.
...does that mean the comments in question were in violation of these rules, or just that they perhaps exposed uncomfortable yet real weaknesses of the work? Asking the real questions here.
Many of the answers here suggest that you should not respond to low-quality public criticism. This is a good approach. An alternative approach is to reply with:
Thank you for your interest in my research.
This reply has two functions.
