We all can probably say from personal experience that anonymous commenters can behave pretty badly. There is scientific evidence to back this up. A study published last year  showed staggering differences in the quality of comments on news websites when readers could post anonymously. When comments were not anonymous, they were classified as "uncivil" around 29% of the time. When comments were anonymous, that jumped to over 53%!
A study published a couple months ago  confirmed this by comparing political discussions on the Washington Post website, which is mostly anonymous, with comments about the same topics on the Washington Post's Facebook page. The Facebook comments were far more civil.
Psychologically, this behavior is explained by the "online disinhibition effect" . The theory says that anonymity is one of the reasons that people say and do things online that they would never do in person. Since they do not have to face the consequences for their anonymous actions, they feel free to let out an uninhibited version of themselves.
This results in uncivil commenting. More and more news sites are combating this by moving their commenting functionality to Facebook. They either move discussions to their Facebook pages, or require people to use their Facebook identities to comment on the website. Researchers have found that this does indeed increase the quality of comments on articles , which makes news sites happy.
And this is where anonymous commenters have inadvertently caused something very dangerous to happen.
When I wrote a few posts about trolls on this blog, a lot of people commented that they were often called "trolls", when in reality, they were trying to stir up debate on a topic that demanded it*. I'm sure this is true – people who criticize commonly held beliefs (even when those beliefs need to be challenged) might be called "trolls" unfairly. Challenging debate is important to a healthy civil society.
The problem is that the lack of civil discourse among commenters is pushing us away from the opportunity to have those kinds of discussions.
Remember – more than half of comments on sites that allow anonymity are uncivil. Anonymity degrades the quality of discussion dramatically. This forces sites to turn to Facebook to raise the quality of the discussion. That is the first part of the problem.
The second part of the problem is that Facebook does not allow anonymous accounts. In fact, they have started aggressively enforcing their "real name" policy over the last few weeks. If Facebook suspects you are using anything but your legal name – even if you have your professional title in your profile name - they can suspend your account. They are doing a lot of that these days. Yitz Jordan wrote an excellent article about this on Quartz, which you should read.
People have very valid reasons for using fake names. In fact, pseudonyms can be a critical part of challenging the status quo and calling out corruption. Even Hamilton, Madison, and Jay wrote the Federalist Papers under an anonymous pseudonym.
Imagine yourself living in a country with a corrupt government that arrests people who post anything critical of the regime online. Or working for a company here in the US that's owned by people with strong religious views who will fire anyone they catch behaving in a way that is out of line with their beliefs. You may very well want to hide your true identity when you debate policies you disagree with.
Facebook's policy against pseudonyms is dangerous for this reason (and it's behind the times – Google just apologized for their real name policy and removed it). They should change it.
But in the meantime, Facebook is discouraging real debate because they require people to use their true identities in discussions. At the same time, anonymous commenters are pushing news sites toward Facebook with their vitriol. Not only have the uncivil anonymous commenters ruined comment sections for readers (anonymous and otherwise), they have decreased the chances for the important debate that many insist is their goal.
Hopefully Facebook will update their policies so this becomes less of an issue. And we can all hope that abusive anonymous commenters change their ways and engage in civil discourse. In the meantime, I will continue to read your comments on this blog, and follow this advice on Twitter everywhere else.
 Santana, Arthur D. "Virtuous or Vitriolic: The effect of anonymity on civility in online newspaper reader comment boards." Journalism Practice 8.1 (2014): 18-33.
 Rowe, Ian. "Civility 2.0: a comparative analysis of incivility in online political discussion." Information, Communication & Society ahead-of-print (2014): 1-18.
 Suler, John. "The online disinhibition effect." Cyberpsychology & behavior 7.3 (2004): 321-326.
Hille, Sanne, and Piet Bakker. "Engaging the Social News User." (2014).
*For the record, stirring up debate or having a contentious discussion is not trolling. This post describes a researcher's formal definition, which basically says trolling is doing upsetting things just for the joy of watching other people suffer.