I care about the Facebook decision to ban Trump, but I do not have a strong opinion about it. I have heard arguments on both sides now, from up and down, and still somehow... I don't know how I feel. So instead of posting my opinion I post other opinions and my opinion of them.
1) Facebook is a private company. If they want to have liberal bias or a free for all or whatever then it is not the governments place to interfere. If enough people don't like what they see then they will lose customers. The invisible hand of the market will regulate it enough. Libertarians and honest small-gov republicans might believe this. On a personal level, I don't want someone else telling Lance and I that we can't block some comment; however, for now, more people use Facebook then read Complexity Blog.
2) Facebook is a private company but they need to follow standard business practices of having their uses sign an agreement and stick to it. Since the user signed the agreement, Facebook need only stick to that agreement. This is problematic in that (1) if the agreement is not that rigorous then Facebook can be arbitrary and capricious, but (2) if the agreement is to rigorous then people can game the system. Imagine if Lance and me had rule that you could not use profanity in the comments. Then someone could comment
People who think P vs NP is ind of ZFC can go Fortnow themselves. They are so full of Gasarch.
(Something like this was the subplot of an episode of The Good Fight)
3) Facebook is so big that it has an obligation to let many voices be heard, within reason. This could lead to contradictions and confusions:
a) Facebook cannot ban political actors. What is a political actor? (Jon Voight is pro-trump and Dwayne ``The Rock'' Johnson is anti-trump, but that's not what I mean.) High level people in the two main parties qualify (how high level?). IMHO third parties (Libertarian and Green come to mind) need the most protection since they don't have as many other ways to get out their message and they are serious. (I wonder if Libertarians would object to the Government forcing Facebook to not ban them). What about the Surprise Party or the Birthday Party (which did have a platform see here). And what about people running for Mayors of small towns (much easier to do now with Facebook)? Should just running be enough to ban banning?
b) Facebook can ban posts that are a threat to public health and safety. I am thinking of anti-vaxers and insurrectionists, though I am always wary of making them free speech martyrs.
c) Fortunately a and b above have never conflicted. But they could. I can imagine a president who has lost an election urging his followers to storm the capitol. Then what should Facebook do? (ADDED LATER- A commenter points to a case where a and b conflicted that is not the obvious case.)
4) Facebook is so big that it has an obligation to block posts that put people in danger. This may have some of the same problems as point 3---who decides?
5) Facebook is so big and controls so much of the discourse that it should be heavily regulated (perhaps like a utility). This has some of the same problems as above- who decides how to regulate it and how?
6) As a country we want to encourage free speech and a diversity of viewpoints. There are times when blocking someone from posting may be better for free speech then letting them talk. When? When that person is advocating nonsensical views that stifle the public discussion. But I am talking about what the country should want. What do they want? What does Facebook want? Does either entity even know what they want? These are all ill defined questions.
7) Facebook is a monopoly so use Anti-Trust laws on it. Anti-Trust was originally intended to protect the consumer from price-gouging. Since Facebook is free this would require a new interpretation of antitrust. Judicial activism? The Justices solving a problem that the elected branches of government are currently unable to solve? Is that a bad precedent? What does it mean to break up Facebook anyway--- its a network and hence breaking it up probably doesn't make sense (maybe use MaxCut).
(ADDED LATER- a commenter pointed out that anti-trust is NOT just for consumer protection, but also about market manipulation to kill small innovators.)
8) Lets say that Facebook and Society and the Government and... whoever, finally agree on some sort of standards. Then we're done! Not so fast. Facebook is so vast that it would be hard to monitor everything.
9) As a side note- because Facebook and Twitter have banned or tagged some kinds of speech or even some people, there have been some alternative platforms set up. They always claim that they are PRO FREE SPEECH. Do liberals post on those sites? Do those sights ban anyone? Do they have SOME rules of discourse? I ask non rhetorically.